The person spoke Wednesday to The Associated Press on condition of anonymity because the Dolphins had yet to confirm the deal.
The Dolphins will be the third NFL team since December for Incognito. He has started 47 games but concedes he has a reputation for being "a less than model citizen."
Last year the St. Louis Rams benched him 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.
In Miami, Incognito will compete at right guard with Donald Thomas and Nate Garner, who shared the job last year.