Smith had been an unrestricted free agent. He says the team changed its offer, and he decided it was time to make a decision. He accepted a three-year deal.
It's an $18 million deal that includes $8 million this year, a league source told NFL Insider Adam Schefter.
The agreement gave the Bengals freedom to look at other spots in the draft rather than having to worry about replacing Smith, who was a first-round pick in 2009.
He was hurt his first two seasons, but lost a lot of weight and became a steady starter the last two years.
Information from The Associated Press was used in this report.