Rothschild spent the last nine seasons as the New York Yankees' pitching coach. The club announced in late October that he would not return for a 10th.
The 65-year-old has worked on various coaching staffs since 1986. He was the first manager for the Tampa Bay Rays and was later the Chicago Cubs' pitching coach from 2002 to 2010.
Rothschild replaces Darren Balsley, who served in the role since May 2003. Balsley will remain with the organization and serve as a special assistant working with minor-league pitchers, according to Acee.
New manager Jayce Tingler is expected to announce his full staff for the upcoming season sometime next week.