The terms were not immediately disclosed on Monday.
Procter spent five seasons with Dallas, starting 11 games in 2008 and appearing in 12 as a reserve last season. He has played guard and center since coming into the NFL after being a four-year collegiate starter at Montana.
The Cowboys originally signed Procter from the Detroit Lions' practice squad in November 2005.
Procter is the third University of Montana player on the Dolphins roster. Pro Bowl kicker Dan Carpenter and running back Lex Hilliard also played for the Griz.