Rufus, a Harrier Hawk, was taken overnight on Thursday and Friday from a car parked outside the home of his owner.
But his official Twitter account tweeted good news on Sunday night: "We can confirm the news is true RUFUS HAS BEEN FOUND safe and well & reunited with family!!
"Thank you so much for your support.
"We are so overwhelmed by all your support, #findrufus has worked, Rufus is healthy & well... we are SO excited/happy/relieved."
A police spokesman said the car was parked on a private drive in Dunstall Road, Wimbledon, with the rear window open for ventilation, when the thieves struck.
The four-year-old hawk, which deters pigeons at the All England Club simply through his presence, is also a family pet, and his owners were very distressed over his disappearance.
Imogen Davis, 25, said her family reared Rufus as part of the family-run business Avian Environmental Consultants.
"It's a family business, the birds are brought up around us. They're part of the family. It's just the way it is," she said.
Rufus has become a well-known fixture at the south-west London club, with visitors often stopping to ask for photos with the hawk and even tennis stars, including former champion Richard Krajicek, tweeting pictures of him.