The 6-foot-6, 330-pound Clabo spent the past seven seasons with the Atlanta Falcons and was a 2010 Pro Bowl selection. He has 101 career starts, including every game the past five years.
Martin played left tackle at Stanford, where he protected quarterback Andrew Luck's blind side. As a rookie last season, he started 12 games at right tackle, then four at left tackle after Long was hurt.
Miami also signed undrafted rookie linebacker David Hinds, who played at Florida Atlantic.