Rucker agreed to terms on a five-year, $21 million contract Wednesday and signed his deal Thursday after passing a physical. The Cincinnati Enquirer reported the deal includes $8 million guaranteed.
The Browns also made another move Thursday to bolster their defensive line, agreeing to a one-year, $3 million deal with former Philadelphia Eagles defensive end Juqua Parker, a league source told ESPN NFL Insider Adam Schefter.
Rucker had his best season with Cincinnati in 2011, recording a career-high four sacks in 11 starts. He appeared in all 16 games in helping the Bengals make the AFC playoffs.
Browns general manager Tom Heckert says Rucker is a player the team targeted in free agency. Heckert says he's excited to about adding Rucker to a young defensive front with end Jabaal Sheard and tackles Ahtyba Rubin and Phil Taylor.
The Bengals drafted Rucker in the third round in 2006.
Cousins made one start at right tackle last season after the Browns were awarded him off waivers from Baltimore. He has made five career starts and played in 30 games. Cousins gives the Browns offensive line depth after the team released right tackle Tony Pashos, who recently underwent foot surgery and is expected to need 10 months to recover.
Smith made four starts last season. He finished with 14 catches for 131 yards and a touchdown.
The Browns also said defensive lineman Brian Schaefering signed his tender as an exclusive rights player.
Information from ESPN NFL Insider Adam Schefter and The Associated Press was used in this report.