The Ivory Coast striker admitted an aggravated breach of FA Rule E3 in that Anelka's gesture was deemed to have anti-Semitic connotations.
Sagbo posted a picture on Twitter of Anelka's celebration alongside the word: "Legend".
He also referred to Anelka as a role model for France's urban youth.
Hull boss Steve Bruce said two weeks ago that the club would "vigorously defend" the charge but the player since decided to accept the charge.
The FA said in a statement: "Following an independent regulatory commission hearing, Yannick Sagbo has been fined £15,000, subject to any appeal, after he admitted an aggravated breach of FA Rule E3.
"The Hull City player was also warned as to his future conduct and ordered to complete a compulsory education course.
"The charge was that the comment was abusive and/or indecent and/or insulting and/or improper, contrary to Rule E3(1). Further to that, The FA considered the comment to be an aggravated breach, as defined in FA Rule E3, in that it included a reference to ethnic origin and/or race and/or religion or belief."
Both the FA and Sagbo have the right to appeal the decision but it is unlikely either party will do so.