Bour, 30, is hitting .227 with 19 home runs and 54 RBIs in 112 games with the Marlins this season. He has a career .262/.346/.470 slash line over parts of five seasons with the Marlins.
"I envision him being a dynamic, power-hitting weapon off the bench," Phillies manager Gabe Kapler said.
"The numbers against righties are outrageously good and the plate discipline fits right in with our lineup. He knows how to look over the baseball. He attacks it when it's in the zone. He fouls balls off. He fights. He is a tough out," Kapler said.
The Phillies put in a waiver claim on Bour before working out a trade with the Marlins. Miami also sent $466,129 to Philadelphia to cover half of Bour's remaining salary this season in return for getting a better prospect in the deal, a source told ESPN.
Bour has four years of MLB service time and is making $3.4 million this year. He has two years of salary arbitration remaining and was a candidate to be non-tendered by Miami this offseason.
The switch-hitting Carlos Santana has started 112 of Philadelphia's first 114 games at first base this season, so Bour will be primarily a bench bat down the stretch for the Phillies in the team's quest to earn a postseason berth.
Philadelphia began a three-game series in San Diego on Friday night with a one-game lead over Atlanta and six games ahead of Washington.
"I think it's worth noting that he's really hurt the Braves. I think that matters," Kapler said. "And look, he's going to be a really tough out against a right-handed reliever or starter, and we're going to look for ways to be opportunistic in deploying him."
The Marlins are likely to use Derek Dietrich and Miguel Rojas at first base over the final two months of the season. Garrett Cooper is also working his way back from a wrist injury that's sent him to the disabled list twice this season.
Mills has spent the season in Single-A Advanced Clearwater.
Information from The Associated Press was used in this report.