The Frenchman performed the goal celebration after scoring in his club's match against West Ham on December 28.
Anelka denied the gesture had any anti-Semitic meaning and was a signal in support of his friend, the French comedian Dieudonne M'bala M'bala, the person who first brought the quenelle to prominence.
He and a legal team have mounted a defence this week at an independent regulatory commission's hearing at the Grove Hotel in Watford.
The independent regulatory commission said in a statement on the FA website that the two charges Anelka faced - that the gesture was abusive and/or indecent and/or insulting and/or improper, and that it included a reference to ethnic origin and/or race and/or religion or belief - were both found proved.
The FA stated: "An independent regulatory commission has found an aggravated breach of FA rule E3 against Nicolas Anelka proven and has issued a five-match suspension and a fine of £80,000, pending appeal."
Importantly, the commission added that it was their finding that Anelka had not been deliberately anti-Semitic.
The commission statement said: "So far as the basis for our finding on Charge 2 is concerned, we did not find that Nicolas Anelka is an anti-Semite or that he intended to express or promote anti-Semitism by his use of the quenelle."
The punishment is suspended pending a seven-day period in which Anelka may launch an appeal, unless he decides against appealing, the commission said.
The commission said that Anelka, 34, would undergo an education programme following the verdict.
It said: "In consequence of the finding on Charge 2, the player will be subject to an education programme, the details of which will be provided to him by The FA."
Anelka's friend Dieudonne has been prosecuted for inciting racial hatred in France and Dieudonne's supporters have been pictured using the quenelle as an anti-Jewish gesture. The comedian has also been banned from entering the UK.
The case was expected to hinge on whether Anelka had any knowledge of the quenelle's anti-Semitic connotations and also whether he could be found guilty of the charge even if he was not aware of the full implications of the gesture.
The commission determined that, while he may not have grasped the serious nature of the salute, he could still be issued with the five-match punishment, which is the most lenient that could have been imposed under the FA's new anti-discrimination rules.
At the time of Anelka performing the quenelle, the European Jewish Congress claimed the former Arsenal and Real Madrid player should be subjected to the same punishment handed out to those who perform a Nazi salute.
French minister for sport Valerie Fourneyron also condemned the gesture as "shocking" and "disgusting".
Anelka has been insistent all along that, on his part, it was an innocent gesture.
He wrote on Twitter in December: "I do not know what religion has to do with this story", adding that "of course I am neither racist nor anti-Semitic".