The Braves also got cash back from the Cubs in exchange for catching prospect Victor Caratini. Bonifacio and Russell did not play in the Cubs' 3-1 win over Colorado on Thursday afternoon.
''These are two pieces that we really like,'' Atlanta GM Frank Wren said on a conference call. ''In Bonifacio, we got a really versatile bench player who can do a lot of things well. In Russell's case, it's another veteran bullpen arm.''
Russell was in the home bullpen at Wrigley Field when the trade was made. He hugged several of his teammates and coaches - and slapped hands with a few fans - as he exited while the game was going on.
''It's kind of hard to wrap your head around it,'' Russell said. ''It's obviously a shock. I knew things were gonna happen. There's really nothing you can do to prepare yourself for this. It's still kind of weird. I don't know how to feel. There's a lot of excitement, a lot of mixed emotions.''
The 29-year-old Bonifacio hit .279 with 14 steals in 69 games for the Cubs this season. He previously played for Atlanta manager Fredi Gonzalez when they were both with the Marlins.
''He's a guy who gives you a lot of versatility. You can play him anywhere on the field,'' Gonzalez said in Los Angeles. ''You can bring him off the bench or start him if the matchup is right. He's a nice National League player.''
The 28-year-old Russell is 0-2 with one save and a 3.51 ERA in 44 games.
''He's not your traditional left-handed reliever,'' Gonzalez said. ''You can let him run through some right-handers. He's durable.''
Atlanta is in the chase for the NL East title, and the Cubs are last in the NL Central.
The 20-year-old Caratini was selected by the Braves in the second round of the 2013 draft. He hit .279 with five homers and 42 RBIs in 87 games with Class A Rome this season.
''He's a guy we liked in the draft a lot,'' Cubs general manager Jed Hoyer. ''We've said it all along, catching is a weakness in our system and we don't have enough of it.''