The news was announced by Reynolds' agent, Chad Speck.
Reynolds, a fifth-round pick out of North Carolina in 2009, twice lost his starting spot at right guard this past season. He ended the season inactive for the final game against Carolina, which indicated he would no longer be in the team's plans.
Reynolds had one year left on his contract and carried a cap figure of $1,578,750 into 2014. He was due a base salary of $1,285,000 next season.
The Falcons are intent on rebuilding the offensive line for next season after watching Matt Ryan get sacked a career-high 44 times. They could target an offensive tackle in the draft and add a starting guard via free agency.
The addition of Carimi was geared toward bringing in depth on the right side of the line. Carimi could play right tackle or right guard.