Glenn died at the James Cancer Hospital in Columbus, Ohio, where he was hospitalized for more than a week, said Hank Wilson, communications director for the John Glenn School of Public Affairs.
Glenn apologized for his poor eyesight this year at the renaming of Columbus' airport after him. He said then he'd lost some of his eyesight because of macular degeneration and a small stroke. Glenn had a heart valve replacement in 2014.
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Glenn was the third U.S. astronaut in space and the first of them to get into orbit. He circled the Earth three times. The Soviet Union had put a man into orbit a year earlier in 1961.
Glenn then spent 24 years as a Democrat from Ohio in the Senate and briefly made a run for president in 1984. He returned to space in 1998, at age 77, aboard space shuttle Discovery.
He was the last survivor of the original Mercury 7 astronauts.
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The Soviet Union leaped ahead in space exploration by putting the Sputnik 1 satellite in orbit in 1957, and then launched the first man in space, cosmonaut Yuri Gagarin, in a 108-minute orbital flight on April 12, 1961. After two suborbital flights by Alan Shepard Jr. and Gus Grissom, it was up to Glenn to be the first American to orbit the Earth.
"Godspeed, John Glenn," fellow astronaut Scott Carpenter radioed just before Glenn thundered off a Cape Canaveral launch pad, now a National Historic Landmark, to a place America had never been. At the time of that Feb. 20, 1962, flight, Glenn was 40 years old.
With the all-business phrase, "Roger, the clock is operating, we're underway," Glenn radioed to Earth as he started his 4 hours, 55 minutes and 23 seconds in space. Years later, he explained he said that because he didn't feel like he had lifted off and it was the only way he knew he had launched.
During the flight, Glenn uttered a phrase that he would repeat frequently throughout life: "Zero G, and I feel fine."
"It still seems so vivid to me," Glenn said in a 2012 interview with The Associated Press on the 50th anniversary of the flight. "I still can sort of pseudo feel some of those same sensations I had back in those days during launch and all."
Glenn said he was often asked if he was afraid, and he replied, "If you are talking about fear that overcomes what you are supposed to do, no. You've trained very hard for those flights."
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Glenn's ride in the cramped Friendship 7 capsule had its scary moments, however. Sensors showed his heat shield was loose after three orbits, and Mission Control worried he might burn up during re-entry when temperatures reached 3,000 degrees. But the heat shield held.
Even before then, Glenn flew in dangerous skies. He was a fighter pilot in World War II and Korea who flew low, got his plane riddled with bullets, flew with baseball great Ted Williams and earned macho nicknames during 149 combat missions. And as a test pilot he broke aviation records.
The green-eyed, telegenic Marine even won $25,000 on the game show "Name That Tune" with a 10-year-old partner. And that was before April 6, 1959, when his life changed by being selected as one of the Mercury 7 astronauts and instantly started attracting more than his share of the spotlight.
Glenn in later years regaled crowds with stories of NASA's testing of would-be astronauts, from psychological tests - come with 20 answers to the open-ended question "I am" - to surviving spinning that pushed 16 times normal gravity against his body, popping blood vessels.
But it wasn't nearly as bad as coming to Cape Canaveral to see the first unmanned rocket test.
"We're watching this thing go up and up and up ... and all at once it blew up right over us, and that was our introduction to the Atlas," Glenn said in 2011. "We looked at each other and wanted to have a meeting with the engineers in the morning."
In 1959, Glenn wrote in Life magazine: "Space travel is at the frontier of my profession. It is going to be accomplished, and I want to be in on it. There is also an element of simple duty involved. I am convinced that I have something to give this project."
That sense of duty was instilled at an early age. Glenn was born July 18, 1921, in Cambridge, Ohio, and grew up in New Concord, Ohio, with the nickname "Bud." He joined the town band as a trumpeter at age 10 and accompanied his father one Memorial Day in an echoing version of "Taps." In his 1999 memoir, Glenn wrote "that feeling sums up my childhood. It formed my beliefs and my sense of responsibility. Everything that came after that just came naturally."
His love of flight was lifelong; John Glenn Sr. spoke of the many summer evenings he arrived home to find his son running around the yard with outstretched arms, pretending he was piloting a plane. Last June, at a ceremony renaming the Columbus airport for him, Glenn recalled imploring his parents to take him to that airport to look at planes whenever they passed through the city: "It was something I was fascinated with." He piloted his own private plane until age 90.
Glenn's goal of becoming a commercial pilot was changed by World War II. He left Muskingum College to join the Naval Air Corps and soon after, the Marines.
He became a successful fighter pilot who ran 59 hazardous missions, often as a volunteer or as the requested backup of assigned pilots. A war later, in Korea, he earned the nickname "MiG-Mad Marine" (or "Old Magnet A - ," which he sometimes paraphrased as "Old Magnet Tail.")
"I was the one who went in low and got them," Glenn said, explaining that he often landed with huge holes in the side of his aircraft because he didn't like to shoot from high altitudes.
Glenn's public life began when he broke the transcontinental airspeed record, bursting from Los Angeles to New York City in three hours, 23 minutes and 8 seconds. With his Crusader averaging 725 mph, the 1957 flight proved the jet could endure stress when pushed to maximum speeds over long distances.
In New York, he got a hero's welcome - his first tickertape parade. He got another after his flight on Friendship 7.
That mission also introduced Glenn to politics. He addressed a joint session of Congress, and dined at the White House. He became friends with President Kennedy and ally and friend of his brother, Robert. The Kennedys urged him to enter politics, and after a difficult few starts he did.
Glenn spent 24 years in the U.S. Senate, representing Ohio longer than any other senator in the state's history. He announced his impending retirement in 1997, 35 years to the day after he became the first American in orbit, saying "there is still no cure for the common birthday."
Glenn's returned to space in a long-awaited second flight in 1998 aboard the space shuttle Discovery. He got to move around aboard the shuttle for far longer - nine days compared with just under five hours in 1962 - as well as sleep and experiment with bubbles in weightlessness.
In a news conference from space, Glenn said "to look out at this kind of creation out here and not believe in God is to me impossible."
NASA tailored a series of geriatric-reaction experiments to create a scientific purpose for Glenn's mission, but there was more to it than that: a revival of the excitement of the earliest days of the space race, a public relations bonanza and the gift of a lifetime.
"America owed John Glenn a second flight," NASA Administrator Dan Goldin said.
Glenn would later write that when he mentioned the idea of going back into space to his wife, Annie, she responded: "Over my dead body."
Glenn and his crewmates flew 3.6 million miles, compared with 75,000 miles aboard Friendship 7.
Shortly before he ran for the 1984 Democratic presidential nomination, a new generation was introduced to astronaut Glenn with the film adaptation of Tom Wolfe's book "The Right Stuff." He was portrayed as the ultimate straight arrow amid a group of hard-partying astronauts.
Glenn said in 2011: "I don't think any of us cared for the movie 'The Right Stuff'; I know I didn't."
Glenn was unable to capitalize on the publicity, though, and his poorly organized campaign was short-lived. He dropped out of the race with his campaign $2.5 million in the red - a debt that lingered even after he retired from the Senate in 1999.
He later joked that except for going into debt, humiliating his family and gaining 16 pounds, running for president was a good experience.
Glenn generally steered clear of campaigns after that, saying he didn't want to mix politics with his second space flight. He sat out the Senate race to succeed him - he was hundreds of miles above Earth on Election Day - and largely was quiet in the 2000 presidential race.
He first ran for the Senate in 1964 but left the race when he suffered a concussion after slipping in the bathroom and hit his head on the tub.
He tried again in 1970 but was defeated in the primary by Howard Metzenbaum, who later lost the general election to Robert Taft Jr. It was the start of a complex relationship with Metzenbaum, whom he later joined in the Senate.
For the next four years, Glenn devoted his attention to business and investments that made him a multimillionaire. He had joined the board of Royal Crown Cola after the aborted 1964 campaign, and was president of Royal Crown International from 1967 to 1969. In the early 1970s, he remained with Royal Crown and invested in a chain of Holiday Inns.
In 1974, Glenn ran against Metzenbaum in what turned into a bitter primary and won the election. He eventually made peace with Metzenbaum, who won election to the Senate in 1976.
Glenn set a record in 1980 by winning re-election with a 1.6-million vote margin.
He became an expert on nuclear weaponry and was the Senate's most dogged advocate of non-proliferation. He was the leading supporter of the B-1 bomber when many in Congress doubted the need for it. As chairman of the Governmental Affairs Committee, he turned a microscope on waste and fraud in the federal bureaucracy.
Glenn said the lowest point of his life was 1990, when he and four other senators came under scrutiny for their connections to Charles Keating, the notorious financier who eventually served prison time for his role in the costly savings and loan failure of the 1980s. The Senate Ethics Committee cleared Glenn of serious wrongdoing but said he "exercised poor judgment."
The episode was the only brush with scandal in his long public career and didn't diminish his popularity in Ohio.
Glenn joked that the only astronaut he was envious of was his fellow Ohioan: Neil Armstrong, the first man to walk on the moon.
"I've been very fortunate to have a lot of great experiences in my life and I'm thankful for them," he said in 2012.
In 1943, Glenn married his childhood sweetheart, Anna Margaret Castor. They met when they were toddlers, and when she had mumps as a teenager he came to her house, cut a hole in her bedroom window screen, and passed her a radio to keep her company, a friend recounted.
"I don't remember the first time I told Annie I loved her, or the first time she told me," Glenn would write in his memoir. "It was just something we both knew." He bought her a diamond engagement ring in 1942 for $125. It's never been replaced.
They had two children, Carolyn and John David.
He and his wife, Annie, split their later years between Washington and Columbus. Both served as trustees at their alma mater, Muskingum College. Glenn spent time promoting the John Glenn School of Public Affairs at Ohio State University, which also houses an archive of his private papers and photographs.
The Associated Press contributed to this report.