Barry Bonds -- Officially Divorced

Barry Bonds is a single man again ... no asterisk needed ... because his marriage is officially over, TMZ Sports has learned.

The breakup between Barry and Elizabeth Watson Bonds has been going on for YEARS -- she first filed papers in 2009, then they reconciled ... only to split again in 2010 for good.

Now, after 4 years in the court system, an L.A. County Superior Court judge has signed off on the divorce ... meaning 50-year-old Barry is back on the market.

According to the docs, filed in L.A. and obtained by TMZ Sports, Barry and Elizabeth struck a private deal that presumably covers everything from money to custody of their 5-year-old daughter.

The two were married back in 1998 ... many, many hat sizes ago.