Palmer, who had demanded a trade out of Cincinnati saying he would retire before suiting up again for the Bengals, made good on his threat and did not report to training camp.
The Bengals had refused to give into Palmer's demand until Tuesday when they were unable to turn down a first round pick in the 2012 NFL draft and a second round pick in 2013.
In place of Palmer, rookie quarterback Andy Dalton has gone 118 of 189 for 1,311 yards and seven touchdowns in his first five NFL games.
"The principal development has been Andy Dalton, who has shown himself to be one of the best and most exciting young quarterbacks in the NFL. We have a good, young football team, and Andy can be the cornerstone of that team for a long time."
The teams confirmed the deal shortly after the NFL's 4 p.m. (2000 GMT) Tuesday trade deadline.
Despite no playing time this season, Palmer is expected to step right into the starting job in Oakland after number one quarterback Jason Campbell suffered a broken collarbone during Sunday's win over the Cleveland Browns.
Taken by the Bengals with the first overall selection in the 2003 draft, Palmer spent his entire career in Cincinnati posting a record of 46-51 as starter while passing for 22,694 yards and 154 touchdowns, including a career best 32 in 2005.