Incognito has conceded he has a reputation for being "a less than model citizen," but the Dolphins are counting on him to provide more depth and flexibility up front.
Incognito, who has started 47 NFL games, will contend for a starting job at right guard and has also played center and tackle. The Dolphins will be his third NFL team since December.
Last year the St. Louis Rams benched Incognito in two games, each time after he drew two personal fouls. The Rams waived him after the second benching, and he started the final three games for Buffalo.
Incognito was a third-round draft pick by the Rams in 2005, but eventually wore out his welcome in St. Louis. He criticized the Rams' dwindling fan base in 2008, made an obscene gesture to a TV cameraman during practice and encouraged hecklers by cupping his hands to his ears while leaving the field after a loss.
Incognito left Nebraska after his sophomore season and was kicked off the team at Oregon before turning pro.
In Miami, Incognito will compete at right guard with Donald Thomas and Nate Garner, who shared the job last season. The Dolphins were in the market to improve their depth after injuries left them thin in the offensive line the second half of the year.
Incognito is the Dolphins' second new acquisition in free agency. They signed former Arizona linebacker Karlos Dansby to a five-year contract, and remain in the market for upgrades at receiver, safety, outside linebacker and nose tackle.