Capello saddened by Beckham blow
The 34-year-old suffered the injury in AC Milan's 1-0 win over Chievo on Sunday and flew to Finland for an operation performed by one of the world's top specialists.
"So far everything is fine," surgeon Dr. Sakari Orava told Reuters. "The operation went smoothly and nicely."
Orava was asked whether the midfielder would be able to play in the World Cup in South Africa starting on June 11.
"No, I don't think so...healing takes a long time," he said.
Beckham's foot will be in a cast for around six to eight weeks, after which he can start "more vigorous" physiotherapy.
Beckham, England's most capped outfield player with 115 appearances, had been bidding to play in a fourth World Cup.
"I am upset but want to thank everyone for their messages of support," Beckham said on his official website. "I hope to make a swift and full recovery."
England coach Fabio Capello said Beckham's likely absence was a "big blow."
"I am very sad for David that he has suffered this injury," Capello said in a statement on the FA website.
"I spoke with him after the game on Sunday night to offer my support, as did (assistant) Franco Baldini.
"David is a great professional and has worked very hard to be ready for the World Cup, so missing it will be a big blow."
Beckham was getting ready to kick a ball unchallenged late in Sunday's Serie A match when he suddenly pulled up and shouted to the Milan bench 'It's broken'.
"He had a total tear of the left Achilles tendon and that was repaired," Orava added, saying it was unclear where Beckham would go next for the start of his rehabilitation.
"He was actually in quite a good mood. He was smiling and happy that the operation was done, and happy to hear it went fine. He was not at all depressed, that we could see, about the ability to play in the World Cup."
Such is Beckham's status in Britain that even Prime Minister Gordon Brown said he had written to wish him a speedy recovery.
"His name has been synonymous with football in this country for many years and it will be incredibly sad if he was to miss what would have been his fourth World Cup," Brown told radio station talkSPORT.
Beckham, on loan at Milan from Los Angeles Galaxy for a second time, will miss the Serie A run-in with his side a point behind leaders Inter Milan with 10 games left.
Milan chief executive Adriano Galliani reckoned one of the world's most famous players could be out for five or six months.
Beckham is due to return to Galaxy in July but Galliani said the Italian club would love to have him back again next season.
"In the dressing room I hugged him and told him that he could stay with us again next year if he wants," Galliani told Sky television.
Renowned surgeon Orava performed a minor miracle in fixing Alpine skier Peter Fill's Achilles in time for last month's Winter