The comedian’s publicist said the pair married in a “small, private ceremony” last week.
The couple has been together for ten years.
Carr and Drayton got engaged last year after the latter placed an engagement ring in the comedian’s dessert while they were on holiday in Indonesia.
Writing on Instagram, Carr shared a photo of him with Drayton on their honeymoon.
He wrote: “After 10 days of tacos and tequila this sadly is the only thing that fits me. Diet starts manana!”
Speaking to the Sun, a source said: “Alan is hugely eccentric. But when it came to his wedding, he wanted to keep it as private as possible.
“They chose Los Angeles because it’s away from prying eyes and they wouldn’t be recognised — plus there’s no issue with the weather there.
According to the star’s publicist, the pair are “planning a big celebration with all their family and friends” later in the Summer. They added that the pair were “extremely happy.”
When the star got engaged last year he said that Adele would sing at his wedding.
Carr said the proposal came as shock, after Drayton popped the question whilst the pair holidayed in Indonesia.
“He asked me to marry him in Lombok,” Carr told The Sun.
“I went to the toilet and came out to eat dessert,” he explained.
“And then I was like, ‘Oh my God, a filling’s come out, just my luck on holiday.’
“I pull it out and it’s this ring and then the man on the organ starts singing Can you feel the love tonight?
“Then the chef, all the staff came out and the manager and sang Can You Feel the Love Tonight, but they didn’t know the next lyric, so they just sang, ‘Can you feel the love tonight? Can you feel the love tonight?’
“So it was my idea of hell, but of course I said yes.”
Carr initially promised a huge wedding and says he is going to rope in close friend Adele to provide the entertainment.
“The engagement only happened last week so I don’t know exactly what we’ll do,” he added.
“But a big old wedding and we’ll get Adele singing Someone Like You.”
Fans of Carr congratulated the couple on his Instagram page.
One wrote: “Shout out from the U.S. (Pennsylvania), you have quite the gift of humor! Good wishes to the two of you. Adorable.”
Another added: “Congratulations on your wedding, delighted for you both.”