It went down Tuesday morning in L.A. Superior Court ... TMZ has learned. The divorce had been mediated by a private judge and that judge signed off on the divorce earlier this month, but it needed to be entered into the court system by a sitting judge, which happened this morning.

As for why this divorce took so long, it's a combination of lack of motivation and a very complicated property settlement agreement. As we reported, both Arnold and Maria moved on years ago ... they both have been in relationships but stayed cordial with each other ... and often had family gatherings with their 4 kids.

The rupture in the marriage occurred more than a decade ago, when news leaked that Arnold had fathered a child with the family's housekeeper. That child -- now an adult -- Joseph Baena, is now a college grad with acting ambitions, and he has a leg up because he's the spitting image of his dad.

As for the property settlement ... well, it's all confidential. But, we know there was a ton of money -- an estimated $400 million -- and our sources say things pretty much got divided down the middle. There was no prenup.

Arnold and Maria were married in 1986, so it was a long run.