Clements started 16 games last season and had one sack and three interceptions.
"He's been a great cover corner," Bengals coach Marvin Lewis said. "He just wanted to get in a situation where he felt good and comfortable. I'm glad it worked out the way it did. He wanted to make sure he wasn't -- as he termed it -- going to play some place that was rebuilding. He wanted to be a piece that could push everything over the top."
"Anybody that's ever spent any time around Nate talks about his professionalism and preparation and everything that way," Lewis said. "You watch him play and you see how smart a player he is. So I think that will be fine. That's not been an issue."
What is an issue is possibly losing linebacker Roddrick Muckelroy, who said he ruptured an Achilles' tendon Saturday night during the first practice of training camp and will be out for the season.
Muckelroy tweeted after Saturday night's practice that he had sustained the injury, which the team declined to confirm.
"My season over b4 it could even start!" he tweeted. "I'm a strong person though I can get pass this hard spot in life (hash)56 for life!"
Muckelroy was a fourth-round draft pick out of Texas last year. He played in 14 games, mostly on special teams, and ranked second in special-teams tackles.
The Associated Press contributed to this report.