The 31-year-old Clements became a free agent on Thursday, when San Francisco released the veteran cornerback. Clements was Buffalo's first-round pick in 2001 and played for the Bills through 2006. He was the 49ers' top defensive signing in March 2007.
Clements started 16 games last season and had one sack and three interceptions. The Bengals needed another cornerback after Joseph signed with Houston earlier in the week.
The 10-year veteran started every game for the Niners during a disappointing 6-10 campaign last season. He returned in 2010 after missing the final nine games in 2009, when he broke his right shoulder blade in San Francisco's 18-14 loss at Indianapolis on Nov. 1 that year.
San Francisco was eager to see more big plays from Clements last season after giving him an $80 million, eight-year contract in March 2007. The former first-round pick by Buffalo was among the most prized players available in free agency that year and often matched up with top opposing receivers.
Clements finished with 82 tackles, one sack, three forced fumbles and three interceptions last season. He also had a major gaffe that led to San Francisco's fourth straight loss to start the year, fumbling after making a key interception late in a 16-14 loss to Atlanta.
Information from The Associated Press was used in this report.