The star was forced to pull out of a series of shows after being diagnosed with appendicitis last month, however he has vowed to return to the stage next month.
He underwent the operation at Monaco's Princess Grace Hospital on Thursday and is understood to be recuperating at his home in Nice, France.
On the mend: Sir Elton John had his appendix removed on Thursday and is recovering at home
The newspaper reports that a source close to him said: ‘Elton is back in Nice playing with the boys now. He is a lot better and very positive after the operation.
‘He still has to rest up but is determined to get back on the road next month and can’t wait to see his fans who have sent thousands of get well soon messages.’
Return: Elton is set to make his first public appearance on September 2 when he picks up an award
He will then open the First Direct Arena in Leeds two days later on September 4.
Last month the veteran musician said he felt ‘grateful to be alive’, revealing that he could have died at any time while struggling through his European tour unaware he was suffering from the condition.
Sir Elton, 66, told The Sun: ‘I was a ticking time bomb. I guess I could have died at any time.
‘I feel so lucky and grateful to be alive.’
Home comforts: Elton is spending time at home with his husband David Furnish and their two sons
Thanks: Elton released a statement thanking his fans for their well wishes
A statement on behalf of the singer said he had been diagnosed with an ‘appendix abscess surrounding retrocaecal appendicitis’.
He is expected to be well enough to attend an event in central London on September 2 at which he will perform and welcome a number of guests.
The Rocket Man and Your Song star is to be the first to be handed the Brits Icon Award.
In a message on his official website, Sir Elton thanked his fans for the support they had shown.
‘I would like to thank the literally thousands of people who have sent me get well cards and messages over the past two weeks,’ he wrote. ‘Your well wishes have touched me deeply and will play a big part in my recovery.
‘I cannot wait to see you all and thank you in person when I resume my concert schedule later this year. In the meantime, please know that I consider myself a very blessed man to have such caring and considerate fans.’
It is the latest health scare for the singer, who last year cancelled a number of shows as a result of a respiratory infection which struck him during a series of US dates. He also missed concerts due to a bout of food poisoning.
In 1999 he had a pacemaker fitted after doctors found he had an irregular heartbeat.
Sir Elton has recently been promoting his forthcoming album The Diving Board, which is due to be released on September 16.
It is his first studio recording of new solo material since his 2006 album The Captain & The Kid. His most recent album was his 2010 collaboration with Leon Russell, called The Union.