Charlie Sheen and Brooke Mueller's divorce was finalized by a Los Angeles Superior Court judge on Monday, legal documents show.

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They had married May 30, 2008, but had been living apart since Christmas 2009 when Sheen was arrested for allegedly assaulting Mueller. Sheen pleaded no contest to a battery charge last year and was placed on probation.

Both Sheen and Mueller have since been in and out of rehab, seeking treatment for their addictions to drugs and alcohol.

UsMagazine.com said they will share legal custody of their twin 2-year-old sons, with physical custody going to Mueller and Sheen granted visitation rights.

The actor is to pay Mueller $55,000 a month in child support. Mueller also received a one-time payment of $757,698.70, a 2009 Mercedes and $1.2 million for her share of the family home, which Sheen will keep.

Mueller waived her right to seek spousal support, UsMagazine.com said.