Fans from Besiktas's main fan group Carsi had played a leading role in May-June 2013 protests against then prime minister now President Recep Tayyip Erdogan.
They had been charged with seeking to overthrow Erdogan's government in a coup and forming a criminal gang, with the trial starting on December 17.
The suspects, who risked being jailed for life if found guilty, were not remanded in custody.
But the Istanbul court acquitted all 35 suspects on all charges of forming a criminal gang, resisting police, and staging an illegal protest, the Dogan news agency reported.
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The anti-government protests began in May 2013 in Istanbul over plans to redevelop Gezi Park on Taksim Square in the centre of the city.
But they then snowballed into a nationwide wave of anger against the Islamic-rooted rule of Erdogan and his Justice and Development Party (AKP).
At least eight protesters were killed and 8,000 injured in a bloody police crackdown.
Founded in 1903, Besiktas is still one of the top Turkish sides and its fans have long been known for staunchly leftist and anti-establishment views.
The acquittal comes after an Istanbul court in April acquitted 26 leaders of Taksim Solidarity, an umbrella group who helped launch the mass protests.