Spain's all-time leading scorer has said he was targeting returning for a possible Champions League final on May 19, and being able to help his national team defend their European Championships title in Poland and Ukraine in June.
"The surgery went fantastically well," Barca doctor Ricard Pruna told a news conference.
"He has been sending messages to his colleagues and laughing with his wife. I have never seen someone in such good spirits after an operation."
Villa broke his left tibia while playing the Club World Cup semi-finals with Barca in Japan last Thursday, and specialist Ramon Cugat said the 30-year-old had been suffering beforehand from a stress fracture.
"Some players can finish their professional careers with a stress fracture," Cugat said. "Players prefer not to have the operation so as not to lose four or five months. Normally no one wants to have preventative surgery.
"Everyone hopes he will be able to play Euro 2012. It's a little tight for the Champions League final in Munich. If I gave a date for his return I would probably be wrong. It will be his leg that decides."
Barcelona won the World Club Cup beating Brazil's Santos 4-0 in Sunday's final, and returned to Spain on Monday afternoon.
