Twombly, who had cancer, died in Rome, said Eric Mezil, director of the Lambert Collection in Avignon, France, where the artist opened a show in June. Twombly had lived in Italy since 1957.
"A great American painter who deeply loved old Europe has just left us," French Culture Minister Frederic Mitterrand said in a statement. "His work was deeply marked by his passion for Greek and Roman antiquity, and its mythology, which for him was a source of bottomless inspiration."
Twombly was known for his abstract works combining painting and drawing techniques, repetitive lines, scribbles and the use of words and graffiti. He is often linked to the legendary American artists Jasper Johns and Robert Rauschenberg, whom he met as a student in New York in the early 1950s.
"Whether it's making sculpture or working across canvas or making small drawings with quite elaborate and detailed elements in them, you have this very strong sense of the physical presence of these paintings and sculptures, and you have the sense of an artist at work," the Tate's director Nicholas Serota said in an in-house interview ahead of a 2008 show of his work.
Though recognition came late for his work -- and he was often overshadowed by the famous company he kept, like Johns and Rauschenberg -- Twombly was asked to paint a ceiling of the Louvre museum in Paris in 2010, the first artist given the honor since Georges Braque in the 1950s.
For that work he chose something simple: a deep blue background punctuated with floating disks and emblazoned with the names of sculptors from ancient Greece, apt for a gallery of bronzes.
"I got into something new in old age," he said of his choice of color, which was unusual.
The Lexington, Virginia-born artist said he was inspired by the colors he found in a Chinese print as well the blue of early Italian Renaissance artist Giotto, who used paint made from lapis lazuli.
"I was just thinking of the blue with the disks on it, it's totally abstract. ... It's that simple," Twombly told The Associated Press at the time.
Simple or not, his work fetched millions at auction: An untitled Twombly painting set an auction record for the artist at a 2002 Sotheby's sale, fetching euro5.6 million. Before that, a 1990 Christie's auction set a record for Twombly, with his 1971 untitled blackboard painting going for $5.5 million.
His canvases also ignited the passions of his followers. In 2007, a woman was arrested in France for kissing an all-white canvas he painted, worth about $2 million. Restorers had trouble getting the lipstick off, and she was ordered to pay hundreds of dollars to the owner and the gallery -- and $1.50 to the artist himself.
Born Edwin Parker Twombly in 1928, the artist got his nickname from his father, who was a baseball player for the Chicago White Sox and had been called Cy after another famous slugger, "Cyclone" Young. Eventually Twombly Jr. got the same nickname.
Between 1942-46, he studied modern European art under Pierre Daura, a Spanish artist who was living in his hometown of Lexington, according to a catalog for a 2009 Twombly exhibit in Rome organized by the Tate Modern and Rome's National Museum of Modern Art.
In 1950, he won a scholarship to the Art Students League in New York, where he was exposed to the works of Rothko, Pollock and others. There he met Rauschenburg, a few years his senior but also a student at the League. On Rauschenburg's advice, Twombly enrolled at Black Mountain College in North Carolina, the experimental school whose alumni are a Who's Who of contemporary arts.
He opened his first solo exhibit at the Seven Stairs Gallery in Chicago in 1951 and a year later sailed from New York with Rauschenburg for his first trip to Europe -- which would eventually become his home -- and North Africa, the catalog said.
In 1954, he was drafted and trained as a cryptographer in the U.S. Army. While serving, he would draw in the dark -- following a Surrealist technique -- and the practice was later evident in his work.
Three years later he moved to Rome and never really left. Later in life, he spent more time in the seaside town of Gaeta south of the Eternal City.
In 1959, he married Luisa Tatiana Franchetti and they had a son, Alessandro Cyrus, the catalog said.
Twombly, who had a gallery in his name at the Menil Collection museum in Houston, Texas, won a series of awards, including a knight in France's Legion of Honor bestowed at the inauguration of the Louvre ceiling.
He won Japan's highest and most prestigious art award in 1998, the Praemium Imperiale prize, which honors fields not covered by the Nobels.
In 2001 he snapped up the prestigious Golden Lion award at the Venice Biennale, where he first exhibited his work in 1980.
The same year, he opened his first major sculpture show at the National Gallery of Art in Washington, D.C. The exhibit was still able to ignite the old controversy about whether what he made was really art and whether what he possessed was really talent.
To some it looked like the debris in a carpenter's shop with planks and crudely nailed boxes slathered with white paint and plaster. For others, it was an eloquent reminder of the ancient Mediterranean.
"In painting, drawings and sculpture, Cy Twombly constantly held himself apart from the great conflicts that would upset the artistic scene of the 20th century," Mitterrand said.
Mezil, the Avignon gallery director, said that his work only got better with time. Twombly's June show there was "the most beautiful exhibit before his death," he said.
Funeral arrangements were not immediately known.