The Packers and McKinney agreed to terms on a four-year, $68 million contract Monday, Adam Schefter of ESPN reports.
McKinney will not receive the transition tag from the Giants and will become a free agent at the start of the new league year, March 13, Mike Garafolo of NFL Network reports.
McKinney recorded 12 tackles (eight solo) during the Giants' 31-19 win over the Commanders on Sunday.
McKinney (ribs) was a full participant at practice Thursday, Dan Salomone of the Giants' official site reports.
McKinney registered 10 tackles (eight solo) in Sunday's Week 10 loss to the Cowboys.
McKinney played in one of the Giants' three exhibition games, logging 21 snaps on defense against Carolina in Week 2.
McKinney played in nine games during the regular season, totaling 45 tackles (29 solo), including one sack. He added five defended passes and a forced fumble.
McKinney recorded seven tackles (four solo) and a pass defended on 46 defensive snaps in Sunday's 38-10 win over Indianapolis.
The Giants activated McKinney (hand) from the NFI list ahead of Sunday's game against Indianapolis, Michael Elsen of the team's official site reports.
The Giants announced Thursday that McKinney (hand) has been designated for a return to practice from the reserve/non-football injury list, Jordan Raanan of ESPN.com reports.