The Beatles legend tied the knot with Nancy Shevell at London's Marylebone Register Office – the same venue where he tied the knot his late first wife Linda in 1969 – and took to his guitar to perform a song he had written for her for the big day.
Following the nuptials, the 69-year-old star clutched the 51-year-old heiress' hand and said: "I feel absolutely wonderful. I feel terrific. I feel married."
Paul - who was marrying for a third time - paid tribute to his "soulmate" Nancy when the newlyweds emerged from the ceremony, where they were cheered by hundreds of wellwishers.
Nancy wore a long-sleeved dress in Ivory silk – which was designed by Paul's fashion designer daughter Stella McCartney – and she sported a single bloom in her hair, while the groom wore a dark blue suit and tie.
Among the 30 guests at the wedding were Paul's former Beatles bandmate Ringo Starr - who was accompanied by his wife Barbara Bach - and George Harrison's widow Olivia.
Paul's seven-year-old daughter Beatrice - from his second marriage to Heather Mills, who he divorced in 2008 - acted as bridesmaid.
The music legend paid tribute to Linda at the reception, which was attended by around 100 guests including Kate Moss, Ronnie Wood, David Gilmour, Jeff Beck, Twiggy, Jools Holland, Tracey Emin, Sharleen Spiteri and David Frost.
Mark Ronson acted as DJ for the event, which saw guests enjoy £110-a-bottle organic champagne.
Paul chose the wedding date because it would have been the 71st birthday of the late ex-Beatles singer John Lennon, who was shot dead in New York in 1980.