Cameron and Tyler Winklevoss have decided not to appeal their $65 million settlement with Facebook.
The Olympic rowing twins signalled a possible end to the long-running dispute with the social network and its founder Mark Zuckerberg when they announced that after "careful consideration" they would not seek Supreme Court review.
The 2008 settlement was intended to resolve a feud over whether Zuckerberg stole the idea for what became the world's most popular social networking website from the Winklevosses, fellow Harvard University students.
Their battle was dramatized in the 2010 film "The Social Network".
After agreeing to the cash-and-stock accord, the Winklevosses sought to undo it, saying it was fraudulent because Facebook hid information from them and that they deserved more money.
The 6-foot 5-inch twins, who competed in the 2008 Beijing Olympics, had been planning to appeal an April ruling by a federal appeals court in San Francisco upholding the settlement, which that court called "quite favorable", but ended the appeal this week.
The filing this week did not give a reason for the decision.
Zuckerberg created Facebook in 2004 in his Harvard University dormitory room.
The California case had been brought by ConnectU Inc, which the Winklevosses set up with another Harvard student, Divya Narendra, who joined in this week's filing.
"We've considered this case closed for a long time, and we're pleased to see the other party now agrees," Facebook said in a statement.
Facebook can now seek the dismissal of a related lawsuit filed in Boston federal court.
Analysts have estimated that Facebook could be worth $70 billion or more should it conduct an initial public offering, perhaps in early 2012.
Facebook could be worth more than $100 billion in an IPO, CNBC television estimated last week.
Jerome Falk, a lawyer for the Winklevosses and Narendra, did not immediately return requests for a comment.