Kurcz was the Cubs' 10th-round pick in 2010 and went 5-4 with a 3.28 ERA in 32 games last season with Class A Daytona. He struck out 139 over 109 2/3 innings and walked 45.
The Cubs sent pitcher Chris Carpenter to the Red Sox on Feb. 21 and, at that time, the two teams also agreed to exchange Minor League players to be named. The Red Sox still owe the Cubs a Minor League player to complete the transaction.
Epstein had one year remaining on his contract with the Red Sox at the time he joined the Cubs in late October as president of baseball operations.