Moreno, 29, pitched in four games over two stints with the Yankees in 2015. He was 0-0 with a 1.10 ERA in 11 appearances for the Bulls, including five saves in five opportunities. He had 17 strikeouts in 16 1/3 innings with just three walks.
"Diego's a guy who we really liked during Spring Training," Rays manager Kevin Cash said. "Showed some pitchability, obviously had a big fastball, and he's done a nice job since he got to Durham, so we're excited to have him up here."
Moreno will become the sixth non-roster invite to Spring Training to appear for the Rays this season, joining right-hander Tommy Hunter, Marks, outfielder Shane Peterson, catcher Jesus Sucre, and first baseman Rickie Weeks Jr.