The 30-year-old, who picked up the injury in the latter stages of last season, was present for pre-season training with the Welsh outfit on Tuesday.
"I had the operation three-and-a-half weeks ago in Germany, done by a lady over there who is world renowned," Britton told Wales Online.
"It went well and literally six days later I was back on the training ground working on building up the muscles around the area where it's been repaired.
"I've been in training for the last two weeks really and on the training pitch the last three days, running, twisting and turning like we'd normally do. I'm pretty much fully fit."
Britton made 33 league appearances for Swansea last season.