Chad Johnson and Evelyn Lozada are officially divorced ... Lady Detective has learned.

A judge in Florida signed off on the divorce early this morning ... one month after Evelyn filed for divorce from the NFL star.

As we previously reported, Chad initially didn't want to sign off on the split ... and waited until last week before finally accepting reality and submitting divorce papers of his own.

But Evelyn claimed the marriage was irretrievably broken after he allegedly headbutted her in the face during an argument over a condom receipt she found in his car.

Chad has since had Evelyn's face tatted on his leg ... and insists he will eventually repair the relationship.

Sources close to Evelyn tell us it ain't gonna happen.