Barney, 28, was designated for assignment last Tuesday when Emilio Bonifacio was activated from the disabled list. Barney lost his starting job early this year as Bonifacio got off to a hot start.
Barney was a 2012 Gold Glove winner and is considered one of the best defensive second basemen in the game.
"He was going to land on his feet," Cubs manager Rick Renteria said Monday afternoon. "It's tough in the moment when change occurs but we've been in this game a long time, he's been around a while and done well. He's found a new club. Hopefully it goes well for him.
When Bonifacio went down with an oblique strain last month, Barney started playing more and was hitting .385 in July. But a two-day paternity leave opened the door for rookie Arismendy Alcantara, who was called up in Barney's place.
A fast start for Alcantara has turned into a permanent job, leaving Barney to be demoted. Barney was hitting .230 with two home runs and 16 RBIs in 72 games this season. He's a career .244 hitter.