James Martin/CNET

Tyler and Cameron Winklevoss and partner Divya Narendra have decided to drop their long-running legal dispute with Facebook and CEO Mark Zuckerberg and accept their $65 million settlement.

The twins and Narendra, classmates of Zuckerberg at Harvard, announced last month it would ask the U.S. Supreme Court hear their case against the social-networking giant and its co-founder. However, in a filing today with the 9th U.S. Circuit Court of Appeals, they said that "after careful consideration," they would not file their petition with the Supreme Court.

Facebook applauded the decision to drop the case.

"We've considered this case closed for a long time, and we're pleased to see the other party now agrees," a Facebook spokesman said.

The petition stemmed from a settlement the Winklevosses and Narendra signed with Facebook in 2008 after claiming Zuckerberg stole their idea for a social-networking site they called ConnectU. The trio accepted a $65 million settlement from Facebook and Zuckerberg in exchange for dropping all further litigation against the site but later said the settlement was based on an inaccurate valuation of the company.

Facebook, which is now reportedly worth more than $100 billion, rejected their claims, saying that the Winklevosses and Narendra received their fair share. (The conflict was depicted in the Academy Award-winning film "The Social Network," released in 2010.)

The 9th U.S. Circuit Court of Appeals agreed with Facebook and Zuckerberg in April, upholding the 2008 settlement. That lead Winklevosses and Narendra to announce their intention to appeal their case to the U.S. Supreme Court.

However, the filing doesn't settle all legal challenges concerning Facebook's origins. A New York man claimed in a 2010 lawsuit that he has a contract with Zuckerberg that entitles him to a 50 percent stake in the social-networking giant. Facebook and Zuckerberg have called the lawsuit a "fraud."