The identical twins, both Olympic rowers, had been appealing an earlier decision that they couldn't back out of a previous settlement with Facebook - now worth over $160million - despite their claim that Facebook had misled them over its value.
Throwing out their appeal, Judge Alex Kozinski wrote: 'At some point, litigation must come to an end. That point has now been reached.'
As depicted in the David Fincher film, the twins - Cameron and Tyler Winklevoss - were contemporaries of Mark Zuckerberg at Harvard who tried to hire him to code their own social networking site, HarvardConnection, and then accused him of stealing the idea after he set up Facebook instead.
The ensuing legal battle formed a large part of the basis for Aaron Sorkin's Oscar-winning script for The Social Network, where the twins were both played by Armie Hammer.