Richard Matt, 49, was killed in the upstate town of Malone, less than 10 miles (16 kilometers) from the Canada border, officials said.
New York State Police Superintendent Joseph D'Amico said authorities found Matt near a cabin after he apparently had fired at a passing camper van.
D'Amico did not say why Matt would shoot at a vehicle, but the New York Times cited a source as saying he was attempting to carry out a carjacking.
"We were able to get into the cabin, where we discovered the smell of gunpowder and realized a weapon had been fired," D'Amico told reporters.
"As we were doing the ground search in the area, there was movement detected by officers on the ground... A tactical team from Customs and Border Protection met up with Matt in the woods, challenged him, and he was shot dead by Border Patrol at that time."
Officers recovered a 20-gauge shotgun from Matt's body.
D'Amico said Matt's fellow escaped killer, 35-year-old David Sweat, was still at large.
The men busted out of Clinton Correctional Facility, about 40 miles from Malone, on June 6 in a spectacular, Hollywood-style prison break.
CNN reported a law enforcement source as saying authorities believe Sweat is "contained."
'Killed, dismembered his boss'
The inmates used power tools to cut their way out of their prison cells before dawn on June 6, triggering an intense weeks-long manhunt across the heavily wooded surrounding area.
"You never want to see anyone lose their life," New York state Governor Andrew Cuomo told reporters.
"But I would remind people that Mr Matt was an escaped murderer from a state prison. Mr Matt killed two people who we know about. Mr Matt killed his boss in a dispute and dismembered him."
The audacious escape sparked a huge search involving more than 1,100 personnel backed by sniffer dogs and helicopters to find the men, who had been spotted in several locations in recent days in upstate New York.
Officers found candy wrappers and other items believed to have been linked to the men and reports emerged that a shotgun was missing from a remote cabin.
Two prison workers have been charged over the brazen breakout, and are accused of smuggling tools and contraband items to the pair in hamburger meat.
Matt and Sweat used the power tools to cut through cell walls and crawled through pipes to emerge from a manhole in the village of Dannemora, home to the sprawling prison.
Matt, six feet (1.83 meters) tall with multiple tattoos, was serving a sentence of 25 years to life for the 1997 kidnapping and dismembering of his former boss in a 27-hour ordeal.
He fled to Mexico after the murder and killed another American there, before being sentenced to 20 years and extradited back to New York.
Sweat was serving a life sentence without parole for murdering a sheriff's deputy in New York state in 2002 when he was 22.