http://img2.timeinc.net/people/i/201...impson-240.jpg

They said it wouldn't last ... and they were right -- because Pete Wentz and Ashlee Simpson are officially divorced ... after a judge signed off on the split.

According to court docs filed in L.A. County Superior Court and obtained by TMZ ... the marriage was formally terminated on November 22 ... after a 3-and-a-half year run.

As for the couple's kid -- Bronx Mowgli -- it's unclear how the couple settled their custody disagreement ... because the details of the divorce settlement are being kept under wraps. TMZ previously reported, Pete wanted joint custody of their son ... but Ashlee had checked the box to get primary physical custody.

The former couple also worked out a secret deal regarding the division of their multi-million dollar empire.

As we previously reported, Wentz chalked up the split to the couple simply growing apart.

الله يعطيك الصحة والعافية