The Globe, ESPN and NFL.com, each citing unnamed team sources, reported Gronkowski has been freed of an infection contracted after multiple previous surgeries on the forearm.
He originally sustained the injury in mid-November, then broke the forearm again in the AFC divisional playoff round Jan. 13 against the Houston Texans.
The Globe reported the latest surgery, Gronkowski's fourth, was meant to replace the plate in the forearm. The report said the procedure took place Monday at Massachusetts General Hospital.
Team officials expect an 8- to 10-week rehabilitation period, but cautioned the 24-year-old tight end may miss the start of training camp.
Gronkowski made 55 grabs for 790 yards and 11 touchdowns in just 11 games last season.