Jedd Gyorko hit .247 with 16 home runs and 57 RBIs for San Diego last season.
The deal was first reported by Jon Morosi of Fox Sports.
Gyorko is coming off a season in which he hit .247 with 16 home runs and 57 RBIs for San Diego. He remains under team control for the next four years after inking a $35 million extension in April 2014 that includes a $13 million club option for 2020. He signed the extension after clubbing 23 home runs in 125 games for his rookie season.
The Cardinals will take on $26 million of Gyoroko's salary while the Padres will pay $6.2 million, according to USA Today's Bob Nightengale.
The left-handed hitting Jay, 30, has $6.85 million remaining on his contract before he becomes a free agent after the 2016 season. Jay hit .210 with one home run and 10 RBIs for the Cardinals last season, playing in only 79 games as he dealt with a wrist injury.
- Christopher Chavez