He will wear No. 7.
To add more depth, the Bills also acquired quarterback Thaddeus Lewis via a trade with the Lions, PFT reports. Lewis played with the Browns last season, where he started one game.
Leinart, the Cardinals' 2006 first-round pick, has had a disappointing NFL career. Arizona released him after four seasons, and Leinart spent 2010-11 as a backup with the Texans, before serving in that same capacity with the Raiders last season.
Bills coach Doug Marrone said Saturday that he hopes Manuel, the team's first-round pick in April, is ready for the regular-season opener against the Patriots in two weeks, but there has been no word on how long Kolb could be sidelined.
In related AFC East news, the addition of Leinart means that the Jets will have to look elsewhere for quarterback help. Mark Sanchez suffered a shoulder injury in Saturday's win over the Giants, and the team was reportedly interested in working out Leinart and John Beck.
Of course, if Rex Ryan can wait a few days, there's a good chance Tim Tebow will be available.