The one-year deal is worth $2.5 million and includes a club option, sources said.
Phelps, 32, missed the 2018 season while recovering from Tommy John surgery. He tore the ulnar collateral ligament in his pitching elbow while throwing the final pitch of his last spring appearance while with the Mariners, with whom he was expected to serve as a setup man in 2018.
Phelps spent his first three big league seasons with the Yankees before they traded him to the Marlins following the 2014 season. He pitched two-plus seasons for Miami before a trade to Seattle in 2017.
Phelps is a career 30-33 pitcher with a 3.89 ERA and 520 strikeouts in 553⅔ innings.