"Macaulay and Brenda have loved being together as a family since welcoming Dakota," a source tells PEOPLE.
"The engagement is the natural next step for them. They are excited for their future together," the source adds.
Earlier on Wednesday, PEOPLE confirmed the couple of four years was engaged.
Song, 33, was photographed sporting a diamond ring on her left hand while out and about in Beverly Hills, California, on Monday.
Culkin, 41, and Song met on the set of their movie Changeland in Thailand and were first romantically linked when they were spotted out in July 2017 grabbing dinner at Craig's, an Italian restaurant in Los Angeles.
While the two actors are notable stars, they've kept their relationship relatively private on social media, except for special occasions, like when Song posted a photo of them on a date night in November at an L.A. Rams game.
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"Very few things can get us out of the house and away from our son," she wrote in the caption.
In 2018, Culkin spoke about his relationship with Song and their plans for the future while on The Joe Rogan Experience podcast, revealing he and Song were trying to have a baby.
"This one's a good one, so I'm probably going to put some babies in her in a little bit," Culkin said, laughing. "I mean, we've definitely been practicing."
He continued, saying he and Song have "a good life."
"I have a pretty little family — a pretty girl, a pretty dog, a pretty cat, and all that stuff. We're gonna move," he said at the time. "We're doing the house thing and all that kind of stuff."
When the Home Alone star appeared on the cover of Esquire in February 2020, Song told the magazine what drew her to her fiancé.
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"People don't realize how incredibly kind and loyal and sweet and smart he is," said Song. "Truly what makes Mack so special is that he is so unapologetically Mack."
She continued: "He knows who he is, and he's 100 percent okay with that. And that to me is an incredibly sexy quality."