Borbon, 27, was claimed off waivers from Texas in April. He appeared in 72 games for the Cubs, hitting .202 with three doubles, one triple and one home run.
Borbon was one of a handful of players the Cubs have taken a chance on through the waiver process this year, but the left-handed hitter started only 12 games for Chicago.
After doubling as a pinch-hitter in the ninth inning on Friday, Borbon was thrown out trying to advance to third on a ball in the dirt with the Cubs down by four.
• Many fans want to know the precise end date of Epstein's grand plan and when they can expect to see a winning team at Wrigley Field. But Epstein said on Friday it's important to know that the winning doesn't start just because a host of top prospects might debut around the same time. Instead, winning starts when a team blends the right mix of talented youngsters and veterans.
"Everyone's waiting for these teams that come up with all these prospects now in the big leagues, and I think the expectation is the light goes on and they win right away," said Epstein, mentioning the Royals and Mariners for comparison. "It's a lot harder than that. Young players go through long adjustment periods in the big leagues. Having a roster with so many young players at the heart of the lineup can be a difficult thing. Those are some of the things that we talk about in the office, kind of get ahead of, even if there's no easy answer for it."
• Despite the Major League success of Dodgers outfielder Yasiel Puig this season, Epstein said there's been no talk of speeding up the development of outfielder Jorge Soler, who is currently on the seven-day disabled list at Class A Advanced Daytona.
"No," Epstein said, "they're different players. They had completely different levels of experience in Cuba."
• Kane County first baseman Dan Vogelbach and Double-A Tennessee right-hander Matt Loosen were selected as the Cubs' Minor League player and pitcher of the month for July.
• Black, acquired from the Yankees for Alfonso Soriano, is scheduled to make his debut for Daytona on Friday.
Cash Kruth is a reporter for MLB.com. Follow him on Twitter at @cashkruth. This story was not subject to the approval of Major League Baseball or its clubs.