9:55 AM PT -- It's a wrap ... Faith and Stevie have already done the deed. Multiple sources at the ceremony confirm they tied the knot in their hotel room Tuesday night ... around 10:30 PM.
Pass the champagne!
According to docs, the singer and producer filed for the license in Clark County on Tuesday. The clock's now running, they have one year to tie the knot. But it seems like they won't need that long -- Stevie tweeted Tuesday, "I love you Faith Renee Jordan," and Faith replied, "I love you back Steven Aaron Jordan."
The couple had broken up last year -- but, you know what they say, break up to make up.
TMZ broke the story ... Stevie avoided going to prison for failing to pay child support. He's on the hook for over a million bucks. He also battled a nasty child custody case with his ex, Joseline Hernandez.