The Raiders surrendered a first-round pick in the 2012 draft and a second-round pick in 2013 for Palmer, the Bengals' Web site reported.
Other reports indicated the 2013 pick could become a first-round selection if Oakland wins a playoff game.
The move gives Oakland an experienced replacement for Jason Campbell, who will miss at least six weeks with a fractured collarbone sustained during Sunday's game against Cleveland.
Campbell could miss the rest of the season and the team had no veteran back-ups, prompting the deal for Palmer, who hasn't played for Cincinnati this season.
Palmer, who had four years remaining on his contract with Cincinnati, made good on a threat to retire if the Bengals did not trade him.
He passed for 3,970 yards with 26 touchdowns and 20 interceptions last year as the Bengals went 4-12.
Celebrity Families of 2014 [PHOTOS]