Over 154 games in 2014, Byrd hit .264 with 25 home runs and 85 RBIs.
He is set to make $8 million in the upcoming season and has an $8 million option for 2016, according to Ken Rosenthal of Fox Sports. The option reportedly will vest when Byrd records 550 plate appearances.
The Reds will also receive cash in the deal. The Philles will acquire pitching prospect Ben Lively, a fourth-round pick in the 2013 draft who posted a 3.04 ERA over 151 innings in Single A and Double A in 2014.
The Phillies went 73-89 this season, while the Reds finished 76-86.