Dermot Mulroney and Prima Apollinaare have hammered out their divorce ... and now the court's declared them officially single!

An L.A. County Superior Court judge signed off Monday on the agreement to end their 14-year marriage ... meaning their status as single persons is fully in effect.

We told you in January the actor and Prima reached a divorce agreement, which included what they plan to do with their shared property, child custody, and support for their 2 minor kids, and any spousal support issues. Those deets haven't been made public.

Dermot and Prima's separation appears to have gone smoothly since he filed for divorce last June.

The pair used mediators to get on the same settlement page ... and we're told they're still friends.