The 49ers received a 2018 fifth-round draft pick for Robinson, who was demoted after starting the first seven games of the season.
The Jets' starting cornerbacks are battling injuries, so there's a good chance Robinson will play Thursday night against the Buffalo Bills.
Morris Claiborne hasn't practiced since injuring his left foot on Sunday, and Buster Skrine, who sat out last week with a concussion, remains in the league's protocol. The Jets haven't ruled out either player for Thursday night.
The Jets also see Robinson as a player who could help them in the future. Only 22 years old, he started 13 games over two seasons for the 49ers.
Hoyer, who started his career with New England, is expected to sign with the Patriots barring an unexpected turn, a source told ESPN's Mike Reiss.
Robinson was a fourth-round pick in 2016 by the Chip Kelly regime, but he fell out of favor with the new administration. He recorded one interception, one forced fumble and one fumble recovery this season in San Francisco.
After getting some opportunities to play as a rookie, the Niners hoped Robinson would be able to take on their top cornerback role in 2017. It's a job he had to open the season but he didn't hold it long as he struggled with penalties.
With those issues mounting, the Niners began using rookie Ahkello Witherspoon in a rotation with Robinson and cornerback Dontae Johnson in Week 5 but Witherspoon stepped into the starting role full time on Sunday against Philadelphia.
On Monday, coach Kyle Shanahan confirmed that Witherspoon would continue to start going forward, leaving the writing on the wall for Robinson.
The trade caught Jets coach Todd Bowles by surprise. Speaking to reporters at 3:50 p.m. ET, he said he didn't anticipate any trades before the 4 p.m. deadline. A few minutes later, word of the Robinson trade leaked on Twitter. Bowles, still at the podium, said it was news to him.
"I think [Robinson] fits any defense," said wide receiver Jeremy Kerley, who played for the 49ers last season. "He's a ballplayer, so he can adjust, he can adapt. We'll definitely get somebody in the locker room who is a wildfire. When I say wildfire, he brings a lot of energy."
ESPN's Nick Wagoner contributed to this report.