Now nearing the age he sang about in The Beatles' When I'm 64, he has so far avoided the fate of going bald, wasting away and mending fuses that he predicted in that song.
His birthday was expected to be spent on a tropical island in the Seychelles, where he and his new wife are thought to be honeymooning.
The couple married at an Irish castle the previous week.
They have not publicly revealed where they headed after the ceremony at Castle Leslie, but the Seychelles Broadcasting Corporation reported that they had arrived in the Indian Ocean nation.
The star has said that despite turning 60, he still sees himself as "just a rock 'n' roller", and that he never thought he would be world famous for 40 years.
In an interview with the BBC World Service, he admitted that he sometimes "assumes that retirement is near".
But whenever he thinks about giving up, "I do one gig and I love it", he said.
Sir Paul has been one of the biggest stars in the world since shooting to fame with The Beatles in the 1960s, and has had success with another band, Wings, as well as with solo material.
He has kept writing and performing, being nominated for an Oscar for the song he wrote for the film Vanilla Sky in 2002, and has also branched out into art, poetry and classical music.
He wed landmine campaigner and former model Mills, 26 years his junior, after a three-year relationship.
The ceremony took place in a small church inside the grounds of Castle Leslie, County Monaghan, Ireland, with 300 family and friends present.
Fellow ex-Beatle Ringo Starr, the band's producer Sir George Martin, model Twiggy and actor Steve Buscemi were among the guests.
But there have been rumours that Sir Paul's daughters refused to speak to Heather because their father took off his wedding ring from his first marriage, to Linda, who died in 1998.
Sir Paul's spokesman described the wedding ceremony as "joyful and moving", and the day was rounded off by a spectacular firework display.
The couple were thought to have left the site by helicopter to start their honeymoon.
They are reported to be on the tiny island of Cousine, which was the location for the Oliver Reed film Castaway.