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Beyonce was also reported to have been among guests at the nuptials in swanky country retreat Babington House
Following the ceremony the couple will both take the name Taylor-Johnson.
The bride met her husband, who is 23 years her junior, when she cast him in the John Lennon movie Nowhere Boy, which she directed.
Sam's gown was designed by Sarah Burton, creative director of Alexander McQueen, who created the dress worn by the Duchess of Cambridge for the royal wedding last year.
Meanwhile, her groom was dashing in a bespoke suit by Tom Ford, the designer-turned-film director.
The actor, whose films include Kick Ass, celebrated his 22nd birthday last week.
He and the Turner-shortlisted artist, who is 45, had their first child together, Wylda Rae, in 2010. Their second, Romy Hero, was born in January this year.
Sam has two daughters from her previous marriage to contemporary art titan Jay Jopling, who made millions from his association with British artists such as Tracey Emin and Damien Hirst.
Anjelica, 15, and Jessie, six, made a cameo as Lennon's younger sisters in Nowhere Boy.
The newlyweds live in an £11-million town house in Primrose Hill, London, bought in 2009.
After their engagement was announced at the premiere of Nowhere Boy, Aaron said their loved ones were "really lovely and supportive" of their relationship despite the age gap.
"They know how intensely we feel," added Sam.