Philadelphia claimed Bour on trade waivers and worked out a deal for the 30-year-old, a source told The Athletic's Ken Rosenthal.
Bour is owed about $900,000, which is the remainder of his $3.4 million salary this season, Rosenthal adds. The Marlins are covering half of Bour's remaining salary, a source told ESPN's Jerry Crasnick.
The powerful first baseman is under team control for two more years after 2018 and has hit well against the Atlanta Braves (.302/.426/.597, 13 HR, 42 RBIs) during his career. The Phillies and Braves are separated by one game atop the National League East standings and are scheduled to play each other seven more times this season.
The Phillies' first basemen are hitting just .218, which is the worst batting average at the position in the NL.
Bour, a left-handed hitter, was hitting .227/.347/.412 with 19 home runs and 54 RBIs in 112 games for Miami, and he's done most of his damage against right-handed pitching.
The Phillies committed $60 million to Carlos Santana to be their first baseman prior to this season. He's hit .219/.356/.402 with 17 homers and 64 RBIs in 114 games.
Mills, 22, was an 18th-round draft selection of the Washington Nationals in 2014. He appeared in 20 games - 16 starts - for High-A Clearwater this season, posting a 2-5 record with a 4.32 ERA and 1.35 WHIP.
To make room on the 40-man roster for Bour, the Phillies designated right-hander Jake Thompson for assignment.