The actress, 34, and American Nick Kocher, 36, enjoyed a lavish bash at Castle Toward in Dunoon, Argyll.
He wore a kilt and arrived at the venue on a speedboat after partying with his friends on a luxury ship before the party.
He spoke of his joy before he was driven in a car through the security gates.
A source said, “They must have spent a fortune. The castle and the private ship were amazing.
Nick looked very handsome in his union. It was the perfect venue for a celebrity wedding.
“No one knows it’s happening.”
Security guards prevented access to the 19th-century walled countryside mound.
Cars are seen being checked before heading towards a sweeping driveway.
The couple made their vows in front of family and fellow celebrities including Karen’s former boss Dr. Who Stephen Moffat and Saturday Night Live comedian Beck Bennett, whose wife, actress Jesse Hodge, gave a read.
It is not clear exactly when the couple formally contracted the contract.
Born in Inverness, Atlanta, Georgia, Karen and Nick are believed to have been dating for over two years after meeting in the United States.
He wrote for the long-running sitcom It’s Always Sunny In Philadelphia and worked alongside his bride on the Netflix movie The Bubble released earlier this year.
Nick shared aboard the Spirit of Fortitude with kilt-clad groomsmen before she set sail.
The groom had to be carried ashore in a canoe across choppy waters after the boat had stopped just 25 minutes before the 3pm service.
Nick said, “It’s amazing.
“I am looking forward to it.
“It’s great to be here.”
Karen has talked about being in a relationship previously but has kept the details under wraps.
It is believed that the couple met in Los Angeles, where she has a home.
They have appeared on red carpets together and left clues about their partnership on social media.
The couple took part in some vacations in Berlin and London.
Karen confirmed that she found love two years ago.
She said: I am not married. I’m in a relationship, but I’m not married, and that’s fine.”
Nick was nominated for his work as a writer on the American graphic show Saturday Night Live in 2017.