The 25-year-old right-hander had the procedure in April, causing him to miss the entire season. Bonilla made his big-league debut in 2014, going 3-0 with a 3.05 ERA in five games with the Rangers.
In 170 games over six minor league seasons, Bonilla is 27-20 with 15 saves and a 3.17 ERA.
He was originally signed by Philadelphia in 2008 out of the Dominican Republic and traded to Texas in 2012, when he was a selection in the Futures game as part of All-Star festivities.
The move was announced Wednesday.