Chris Pratt and Anna Faris Officially Sign Off on Divorce

Chris Pratt and Anna Faris have pulled the trigger on their divorce by signing the final docs that will make them single again ... TMZ has learned.

Sources connected with the couple tell TMZ, they have put their John Hancocks on the papers that will make their divorce final. We're told they will get joint custody of their 6-year-old son Jack. As for the property settlement, as we reported, they have a prenup.

Anna's lawyer, Disso Queen Laura Wasser, asked the judge Monday to remove the case from the court system and have a private judge handle the case instead. The point -- there's a huge backlog in the court system and it takes forever to get a final divorce judgment. A private judge speeds things along.

TMZ broke the story ... Wasser did the same thing for Ben Affleck and Jen Garner ... asking the court to allow a private judge to take over the case.