The Pirates received the pair in exchange for cash, minor league infielder Dilson Herrera and a player to be named later.
Byrd could help make a significant offensive contribution for the Bucs, who came into Tuesday's game against Milwaukee 1/2-game behind National League Central-leading St. Louis.
The 35-year-old is batting .285 over 117 games this season, leading the Mets in both home runs (21) and RBI (71).
Buck, meanwhile, has compiled 15 homers and 60 RBI with a .215 average over 101 games for New York following a quick start to the season.
The 19-year-old Herrera goes to the Mets after batting .265 with 11 homers, 27 doubles and 56 RBI in 109 games with Class A West Virginia.