The foot-long reptile has been nicknamed Malfoy by his rescuers - after Harry Potter’s nemesis Draco.
Experts think the reptile may have been looking for warmth after escaping from his home.
Animal charity the Scottish SPCA is now trying to trace his owner.
The dragon was found on Wednesday in Kilnknowe East End, Earlston. The animal is being looked after at the SSPCA’s rescue centre in Balerno, Edinburgh.
Animal Rescue Officer Steph Grant said: “Bearded dragons require heat so it’s possible Malfoy was seeking shelter in the garage. We’re glad he was found so we could help him.
“He is in good condition so I think there’s a chance he may have escaped from home, although we also have to consider that he could have been abandoned.
“We’re keeping an open mind at this stage and we’re very keen to hear from anyone who recognises him.
“If no-one comes forward for Malfoy we’ll find him a suitable new home.”
Anyone who recognises Malfoy is being urged to contact the Scottish SPCA Animal Helpline on 03000 999 999.