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Johnny Depp and Amber Heard Tie the Knot: Source

02/04/2015 AT 06:55 PM EST

Johnny Depp and Amber Heard made it legal at their home in Los Angeles on Tuesday, a source tells PEOPLE.

As previously reported, a bigger wedding is still to come this weekend on Depp's private island (Little Hall's Pond Cay) in the Bahamas.

Depp, 51, and Heard, 28, got engaged over the holidays in 2012 after meeting on the set of 2011's The Rum Diary.

They stepped out as a couple in 2012 after the actor split with longtime partner Vanessa Paradis, and though they weathered split rumors late last year, the two have seemed better than ever as of late, showing off PDA at various events.

"They're great together," says the source.

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