The happy couple got married over the weekend in Ibiza, sources confirmed to PEOPLE.
The pair exchanged vows at the luxurious La Granja farmstead resort surrounded by friends and family, according to the sources.
In photos on the Daily Mail, both Vikander, 29, and Fassbender, 40, sported bands on their ring fingers on Sunday.
Ahead of the ceremony, Fassbender and Vikander were spotted hanging out with friends and family on the Spanish island Friday, with the Swedish actress wearing a white, summery gown with matching heart sunglasses. Meanwhile, the Irish-German actor showed off his abs in an unbuttoned shirt and a pair of shorts.
Steve McQueen, who directed Fassbender in 2011’s Shame, was photographed at a Friday afternoon party at restaurant Yemanj.
Reps for the couple have not commented.
The actors met in 2014 on the set of their film The Light Between Oceans, in which Vikander prophetically played Fassbender’s wife.
Although rumors that they were dating circulated at the time, the couple remained low-key and kept mum about their relationship. However, they weren’t shy about paying each other compliments on their respective acting talents.
“I knew that Michael was attached to play Tom, and I think he’s one of the most brilliant actors out there,” Vikander told reporters about signing on for her role in The Light Between Oceans.
“I was up for the game, but I was very nervous. I got people that picked me up when I fell and who pushed me. Michael’s support in those scenes were a big part of me daring to go all the way, which was needed for the role of Isabel.”
Fassbender, in turn, praised Vikander’s “fierce” ability.
“I was kind of scared when Alicia came—she was so fierce and hungry,” he told reporters. “I really felt like I had to get my s— together … and just be there and be as present as she was.”
While promoting the movie, the tight-lipped couple spoke with Entertainment Weekly about the importance of keeping their relationship private.
“I think we’ve made a clear statement that we keep certain things just between us,” Vikander said. “It was very easy to unite, but that’s quite personal.”
When asked how they’re able to keep their personal lives out of the spotlight compared with other stars, Fassbender had a very simple answer: “But that’s other people. Each to their own. I’m not going to talk about my private life with a total stranger, unless I feel like I need to. Why would I? I don’t.”
Fassbender and Vikander made their public debut as a couple at the Golden Globes in 2016, where Fassbender said he was “very proud” of his girlfriend’s success (Vikander was a double nominee for her performances in The Danish Girl and Ex Machina).