The Wales international suffered a peroneal tendon injury during his side's 2-1 victory at Sporting Lisbon last week and returned to the UK to undergo an operation to resolve the problem.
Bale is expected to be out of action for the next four months but Real have revealed the operation went well and believe the former Tottenham star has made a good start to his recovery.
A statement on the club's official website read: "Our player Gareth Bale has successfully come through the operation he underwent today after suffering an injury to the peroneal tendons in his right ankle.
"The operation was carried out at London's King Edward VII Hospital by Dr James Calder and Real Madrid Sanitas' Dr Mikel Aramberri, under the supervision of Dr Jesus Olmo, head of Real Madrid's medical department.''
La Liga last week