The Padres have agreed to send right-handed pitchers Luis Patino and Cole Wilcox, as well as catchers Blake Hunt and Francisco Mejia, to the Rays in exchange for the 2018 American League Cy Young Award winner.
Neither team has confirmed the swap, which is pending a physical.
Snell, 28, posted a 4-2 record and 3.24 ERA in 11 games last season for the Rays. He had a league-high 21 wins and American League-best 1.89 ERA in 31 games in 2018. Snell is signed through 2023.
Patino, 21, is the No. 3 prospect in the Padres system. He is the No. 23 prospect in baseball, according to MLB Pipeline. He had a 5.19 ERA and 1-0 record in 11 appearances last season for San Diego.
Wilcox, 21, is the Padres' No. 7 prospect. Hunt, 22, is the Padres' No. 14 prospect. The third-round pick in the 2020 MLB Draft had a 1.57 ERA and 3-0 record in four starts last season at the University of Georgia.
Hunt, 22, hit .255 with five home runs in 89 games in 2019 for Class A Fort Wayne.
Mejia, 25, was the No. 15 prospect in baseball in 2018, when he was traded to the Padres from the Cleveland Indians. He hit .077 with a home run and two RBIs in 17 games last season for the Padres.