Jones who last played for the New England Patriots will stay in the AFC East. The Miami Dolphins claimed the defensive tackle off waivers on Monday.
The four-year player missed all of last season due to a calf injury. He started 23 games spanning from 2013-2014 with New England.
The Bowling Green product was a sixth-round pick by the Houston Texans in 2013, but was released in training camp.
Miami's acquisition of Jones will add depth to what looks like a formidable D-line on paper that includes Ndamukong Suh, Cameron Wake and Mario Williams.
Jones has 79 tackles and nine sacks in his career.