Martin, who protected Andrew Luck's blind side at Stanford, was a second-round draft pick by Miami in 2012. He became a starter as a rookie but struggled at times while being shuffled between right and left tackle.
Last year he was part of a line that allowed a franchise-record 58 sacks. The Dolphins began revamping the line Tuesday by agreeing to terms with Pro Bowl left tackle Branden Albert.
Information from The Associated Press was used in this report.