Gaston spent training camp with Arizona, then was claimed by the Patriots and waived again.
The Dolphins play the Patriots on Sunday in Miami Gardens, Florida.
Gaston was signed by Arizona as an undrafted free agent. He played in 50 straight games at Purdue, 44 of those as a starter.
To make room on the roster for Gaston, the Dolphins waived safety Brandian Ross, who was signed earlier in the week.