Doctors updated the condition of David Sweat from critical to serious on Monday, a day after he was shot after more than three weeks on the run, officials said, and he will be turned over to prison authorities as soon as he is medically cleared.
Sweat, 35, was being treated at Albany Medical Center following his capture on Sunday near the Canadian border.
Fellow escapee Richard Matt was shot and killed on Friday.
The convicted murderers escaped from the Clinton Correctional Facility in Dannemora, New York, where they were discovered missing on June 6.
Sweat will be charged with first-degree escape, according to Clinton County District Attorney Andrew Wylie.
"It's going to be a pretty simple case. We have two holes in the walls of the cellblock," he said.
The men sawed through steel cell walls, climbed a catwalk, crawled through a steam pipe and emerged from an outside manhole, authorities said.
Corrections officer Gene Palmer, who is accused of aiding the escape, appeared in court on Monday in Plattsburgh where a judge granted his attorney's request that the case go to a grand jury.
Palmer, who was stonefaced during the proceedings, is accused of bringing hacksaw blades and a screwdriver bit to the inmates.
Sweat will likely remain hospitalized for a few days before he is turned over to prison authorities, Wylie said.
A New York State Police officer was patrolling alone when he spotted Sweat on a road on Sunday. The fugitive ran, and the officer shot him twice in the torso, police said.
Unarmed, Sweat was captured in Constable, about 40 miles northeast of the prison and less than two miles (3 km)south of the Canadian border.
Matt was shot and killed on Friday some 23 miles away in Duane.
The pair split up five days ago when the younger Sweat decided Matt was slowing him down, New York Governor Andrew Cuomo said.
Matt, who turned 49 the day before he died, had bug bites, blisters and abrasions, according to autopsy results.
The pair planned to drive to Mexico with the help of prison employee Joyce Mitchell, who is charged with helping in the escape, Cuomo said in a WCNY radio interview.
Mitchell has told investigators she was supposed to drive the getaway car but checked into a hospital instead complaining of panic attacks.