Cameron and Tyler Winkelvoss agreed a $65m (£41m) settlement in 2008 after claiming that Zuckerberg stole their idea for Facebook. The legal battle formed the basis of hit movie The Social Network.
In January, the brothers attempted to reopen the case, claiming that they should have received more shares in Facebook.
They attempted to undo the settlement of $20m in cash and $45m in stock, despite the fact that the shares are now worth more than $100m. But a US appeals court ruled in April that they could not get out of the deal.
The brothers threatened to take the case to the US Supreme Court to get the decision overturned, but they have now decided not to pursue it any further. No statement has been issued explaining the decision.
In the original claim, the twins argued that Zuckerberg had stolen their idea after they hired him to code their ConnectU site in 2003.
Facebook vehemently rejected the claims but agreed to the settlement in 2008 to end what it called "rancorous litigation".
Last week, it emerged that Facebook is preparing to float on the US stock market next year, in a move that would value the social network at more than $100 billion (£60.9bn).