Harrison is now recovering in Tuscany, Italy with his wife Olivia.
But he has made an "excellent recovery", according to a statement from his solicitors.
The 58-year-old star had the treatment to remove a cancerous growth from one of his lungs.
The statement said the operation in Rochester, Minnesota, had been completely successful.
Harrison is now recovering in Tuscany, Italy with his wife Olivia.
The statement read: "George Harrison recently underwent an operation on one of his lungs at the Mayo Clinic in the US.
"He is in the best of spirits and on top form - the most relaxed and free since the attack on him in 1999. He is now enjoying a holiday in Tuscany."
Making reference to the star's re-released album, the statement continued: "Although All Things Must Pass Away, George has no plans right now and is still Living In The Material World, and wishes everyone all the very best.
"God bless and not to worry."
Surgery
Harrison has visited the Mayo Clinic, which specialises in cancer treatment, on a number of occasions in the past.
The star was treated for throat cancer in Britain in 1997 after he found a lump on his neck, which he described at the time as "a warning".
He had surgery in August that year, followed by two courses of radiation therapy at the Royal Marsden Hospital near London, the UK's leading cancer treatment centre.
He later said: "I got it purely from smoking. I gave up cigarettes many years ago, but had started again for a while and then stopped in 1997.
"Luckily for me they found that this nodule was more of a warning than anything else. There are many different types of cancerous cells and this was a very basic type."
He had another health scare in December 1999 after being stabbed 10 times by an intruder at his home, resulting in treatment for a punctured lung.
The assailant, Michael Abram was detained indefinitely at a secure hospital after a jury decided he was insane.
The former Beatle made a full recovery from the attack and gave evidence to Oxford Crown Court saying: "I believed I had been fatally stabbed."
Speaking earlier this year, Harrison said: "I had a little throat cancer. I had a piece of my lung removed in 1997. And then I was almost murdered.
"But I seem to feel stronger. I don't smoke any more. I'm a little more short of breath than I used to be, so I don't see myself on stage lasting a full 14 rounds."
His first treatment for cancer was described at the time by Apple Record spokesman Geoff Baker as "a quick operation for a small lump".
It was a 10-minute operation, and Baker said: "As far as he is concerned it is no big deal."
In 1998, the News of the World newspaper quoted Harrison as saying his first brush with the disease made him think about how tenuous life could be. He compared it to "a raindrop on a lotus leaf."
There are three Mayo Clinics across the United States which were founded in the late 1800s.
Their motto is: "The best interest of the patient is the only interest to be considered."
Harrison can have expected the latest scientific advances to have been used in his treatmen and carried out in the most luxurious of surroundings.