Ryan Edward Dougherty, 21; Dylan Dougherty Stanley, 26; and Lee Grace Dougherty, 29, were targets of a nationwide search after they were accused of the crime spree.
Lee Dougherty was shot in the leg after the crash when she pointed a gun at an officer, authorities said. All three suspects were being treated for injuries at a hospital before being transferred to Pueblo County Jail.
"Ladies and gentleman, I'm proud to say we won," Pasco County, Fla., Sheriff Chris Nocco said. "We continuously said that if these three fugitives wanted a battle with law enforcement, we would win that battle. And that's what happened today."
He called the Doughertys "very, very dangerous people" and their capture a tremendous relief.
No troopers were hurt during the 20-mile chase on Interstate 25 that at times exceeded 100 mph. Shots were fired from the vehicle during the pursuit near Walsenburg, 145 miles south of Denver, officials said.
Some of Nocco's deputies were expected to fly to Colorado to interview the trio.
FBI Special Agent Phil Niedringhaus said the three face federal warrants in Florida and Georgia and that Colorado charges were expected. Officials had not decided how to handle extradition.
The siblings' mother, Barbara Bell of East Palatka, Fla., said she had no comment on the arrests. Last week, she urged the trio to give up before there was bloodshed.
A citizen tipped the Colorado State Patrol about 9 a.m. that the suspects were believed to be in Colorado City, about 25 miles north of Walsenburg. Their vehicle was later seen at a nearby campground, but the suspects fled before deputies arrived.
A deputy then spotted the car at a gas station, and the chase began. Troopers deployed spiked stop sticks on the interstate, causing the car to roll over and crash into a guardrail, patrol Lt. Col. Anthony Padilla said.
Two of the three suspects, including Lee Dougherty, were arrested at the scene. A third fled on foot into Walsenburg but was arrested without incident by state troopers.
The arrests came a day after the FBI warned citizens the trio had likely been spotted buying camping gear in Colorado Springs. Alerts went out to dozens of law enforcement agencies.
"I was worried about the safety of our troopers," said Colorado State Patrol Chief Col. James M. Wolfinbarger. "To have them shooting at you and continue the pursuit, those men are brave."
It was a similarly dangerous chase in Florida on Aug. 2 that launched the manhunt.
An officer tried to pull a car over for speeding northeast of Tampa, Fla. A five-mile chase followed, with speeds up to 100 mph, and at least two people in the fleeing car squeezed off 20 or more gunshots.
A bullet burst the patrol car's front tire and the suspects got away, Nocco said. The officer wasn't injured.
Hours later, about 210 miles north along Interstate 75, three people wearing masks charged into Certus Bank in Valdosta, Ga. One of the robbers brandished an AK-47 while another was photographed by a security camera waving a machine pistol, the FBI said.
The robbers fired shots into the ceiling then fled with an undisclosed amount of money in a white sedan similar to the Subaru in the Florida chase.
Sheriff's investigators linked the siblings to the case after they found an ankle monitor near the scene of the car chase. Ryan Dougherty had been issued the monitor after being convicted of sending sexually explicit text messages to an 11-year-old girl. Records show he had registered as a sex offender Aug. 1.
Bell previously told The Associated Press her son was upset by his probation terms and feared the conviction would prohibit him from seeing his newborn son.
Nocco said all three siblings had been living together in Lacoochee, Fla., about 45 miles northeast of Tampa, and each had a criminal record. Lee Dougherty has charges pending against her in Florida for hit and run and had previously been charged with battery, Nocco said, and Dylan Dougherty Stanley had been charged with marijuana possession.
Tracing prior background checks run by gun sellers, police confirmed that Ryan Dougherty bought an AK-47 assault rifle -- like the one used in the bank robbery -- at a pawn shop two years ago. Similar checks showed his brother also owned guns.
Police posted photos of the suspects on electronic billboards across the Southeast. Valdosta Police Cmdr. Brian Childress said it seemed the three had a "death wish."
Lee Grace Elizabeth Dougherty's first brush with the law appears to have been last May after she was involved in a traffic accident on Interstate 95 in Florida's Space Coast.
At the accident scene, Dougherty began screaming and yelling at her boyfriend. Deputies placed her in a patrol car, trying to calm her down, but she kicked and tried to head-butt a deputy, attempted to break out a car window with her foot and spit in the face of a state trooper, according to the accident report.
She was arrested for driving under the influence and battery on a law enforcement officer. She had been driving with a suspended driver's license and she refused to take drug and alcohol tests.
Just 10 days later, she was involved in another traffic accident and charged with driving with a suspended license and leaving the scene of an accident. Her boyfriend, who was in the car with her, was arrested for an earlier domestic violence charge in which Dougherty was the victim. While in the trooper's patrol car, she put a seat belt around her neck and pulled it as if to choke herself, the incident report said.
Lee Dougherty pleaded guilty to the DUI charge and to driving with a suspended license last month. She was sentenced to a year of probation.