The French striker has been banned for five games after he made the controversial gesture in December.
The former France international has also been fined 80,000 pounds for the gesture and has been ordered to complete a compulsory education course.
Anelka has seven days to notify the FA should he wish to appeal against the decision.
In a statement published on its official website, the FA summarized that Anelka "made a gesture (known as the 'quenelle') which was abusive and/or indecent and/or insulting and/or improper, contrary to FA Rule E3(1); and [...] that the misconduct was an "aggravated breach", as defined by FA Rule E3(2), in that it included a reference to ethnic origin and/or race and/or religion or belief".
"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 report stressed.
The incident occurred when the Baggies striker scored against West Ham in a 3-3 draw December 28.
Anelka argued that the gesture, which is claimed to have anti-Semitic connotations in France, was made purely in support of a controversial comedian with whom he is friends.