Burnett will replace Channing Crowder.
Crowder, a six-year starter for Miami, was released Friday following the first practice of training camp to pave the way for Burnett's acquisition.
Burnett, a second-round draft pick by Dallas in 2005, spent four seasons with the Cowboys as a reserve and the past two seasons with San Diego. He started seven games in 2009 and all 16 games last year, when he had 80 tackles, six sacks and two interceptions.
In the first hours of free agency Friday, the Dolphins signed quarterback Matt Moore.
They confirmed the signings of two rookies -- second-round pick Daniel Thomas and fourth-round choice Clyde Gates.
McDaniel, a sixth-year pro, spent the past two seasons with Miami and made a significant contribution off the bench. Trusnik, a fifth-year pro, started a total of 15 games the past two seasons for the Jets and Browns.
Moore is expected to compete with Chad Henne for the starting job at quarterback. He went 1-4 as a starter last year for Carolina.
Thomas is a running back from Kansas State. Gates is a receiver from Abilene Christian.
Information from The Associated Press was used in this report.