They reached a $65m (?41m) settlement in 2008, after claiming that Mr Zuckerberg stole their idea.
The legal spat was immortalised in the film "The Social Network".
In January they attempted to reopen the case, claiming that they should have received more shares than the $45m they agreed on.
They sought to undo the settlement of $20m in cash and $45m in stock - now worth more than $100m.
A US appeals court ruled in April that they could not back out of the deal.
The pair had threatened to go to US Supreme Court to overturn the decision but have now said they will not pursue it.
They offered no statement on what had prompted their decision to abandon the suit.
The twins originally argued that Mr Zuckerberg had stolen their idea after he was hired by them to code their ConnectU site in 2003.
Facebook has always rejected the claims but agreed to the 2008 settlement to end what it called "rancorous litigation".
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