Jessica Simpson's Parents -- Divorce FINAL

Jessica Simpson's parents are officially single and free to mingle ... their divorce is final ... TMZ has learned.

The judge's final touches end a 34-year marriage ... as for why the marriage fell apart -- the speculation continues.

Tina cited "discord or conflict of personalities" when she hit Joe with the papers in Texas last year. As TMZ reported ... Joe became angry after some media speculated he was gay ... and Joe fired back ... calling the reports "ridiculous."

No details yet on who got what ... we've reached out to the family rep -- so far no word back.