Paul Nassif -- Files for Divorce from Adrienne Maloof

"Real Housewives of Beverly Hills" star Dr. Paul Nassif has filed for divorce from his wife Adrienne Maloof ... TMZ has learned.

We broke the story ... Dr. Paul originally filed for legal separation back in July. The divorce docs filed this morning cite irreconcilable differences.

As TMZ previously reported ... Dr. Paul -- repped by powerhouse attorney Lisa Helfend Meyer -- made it clear in the separation docs there is a prenup in place. He also stated he wants joint legal and physical custody of the couple's children. Paul's divorce petition reaffirms that he wants joint custody and acknowledges the prenup. Fact is ... they both have their own money.

Adrienne had planned on filing divorce papers simultaneously with Paul ... but backed out at the last minute. It's unclear if Maloof will ever file the papers ... because it would serve no real purpose.

The couple married in 2002, they have three boys together.