The Bucs optioned right-hander Edgar Santana, who pitched two innings in Tuesday's 8-5 loss to the Dodgers, and brought up Sanchez to bolster their overworked bullpen.
Sanchez, 27, has no prior Major League experience. He will wear uniform No. 59.
A starter throughout his Minor League career, Sanchez moved to the bullpen this year and posted a 3.74 ERA with 65 strikeouts in 55 1/3 innings over 39 appearances for Indianapolis. He was scored upon just twice in his past 15 games since July 4, posting a 1.53 ERA during that stretch.
Originally signed by the Dodgers in July 2010, Sanchez was traded to the Marlins in a July 2013 deal for Ricky Nolasco.