Barry Bonds Officially Divorced

Barry Bonds is a single man again ... no asterisk needed ... because his marriage is officially over


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., 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.

TMZ Sports.