His capture was the dramatic climax of a massive manhunt for Sweat and his fellow inmate Richard Matt, who were discovered missing from the Clinton Correctional Facility in Dannemora, New York, on June 6. Some 1,300 members of law enforcement took part in the search through the forests and bogs of northern New York.
Sweat, 35, was shot and taken into custody in the town of Constable, New York, 23 miles north of Duane, where his accomplice was shot and killed on Friday, New York State Police said in a statement. Constable is just 5 miles south of New York's border with the Canadian province of Quebec.
A state police officer who spotted "a suspicious man walking down a roadway" at about 3:20 p.m. local time, shot and injured Sweat, the statement said. He was taken into custody alive, and then taken to a local hospital for treatment of his injuries.
Details on his condition were not immediately clear. The Buffalo News reported that Sweat was bleeding badly from "life-threatening" wounds, while Plattsburgh's Press-Republican said he was in a stable condition.
CNN showed a photograph of Sweat after he was captured, seated on the ground in a dark jacket and muddy camouflage clothing.
An Albany Times Union reporter said on Twitter that Sweat was taken to a hospital in Malone, New York, and that he would be airlifted to a hospital in the state capital of Albany.
Capturing the suspect alive would enable New York state prison authorities to learn more about how the pair managed to break out and use that information to tighten security.
In their audacious break-out, the pair cut through cell walls, climbed along a catwalk, shimmied through a steam pipe and emerged from a manhole outside prison walls, authorities said.
Matt, 49, was shot and killed on Friday near Malone, about 27 miles (43 km) northwest of the maximum-security prison, by a member of the U.S. Customs and Border Protection tactical unit.
Autopsy results released earlier on Sunday showed he was shot three times in the head and died of severe skull fractures and brain injuries.
Matt also had bug bites, blisters and minor abrasions "consistent with living in the woods for three weeks," the New York State Police said in a statement.
The manhunt for the pair had scoured a remote, heavily wooded area where law enforcement agents worked around the clock in driving rain using infrared devices and listening posts.
The Buffalo News reported earlier on Sunday that Sweat's DNA had been found on a pepper shaker, about a mile from where Matt was shot, citing a law enforcement source. It said pepper is often used by people on the run to try to throw off police dogs.
Sweat had been serving a life sentence without parole in 2003 for killing a New York sheriff's deputy.
Matt was convicted in the 1997 torture, murder and dismemberment of his boss in Tonawanda, New York. After he apparently fired a shot at a passing motorist on Friday, officers spotted and confronted him outside a cabin.
He was shot and killed after he refused to comply with orders to put down a shotgun he was holding, police said.
The Buffalo News has reported that Matt, who turned 49 the day before, may have been intoxicated, citing the owner of a burglarized cabin who said he had found empty liquor bottles.
Police said toxicology results were pending.