The transfer will cost €13m, two years after Emenike left for Russia for €10m without playing a game for Fenerbahce.
The Turkish club announced to the stock exchange that the Nigerian has until August 12 to pass his medical before the transfer will be completed.
Emenike has not hid his admiration for Fenerbahce following his hurried departure last year after signing from Karabukspor for €9m due to match fixing allegations. He has been cleared of all charges.
The Yellow Canaries will have to make room for the 2013 Africa Cup of Nations golden boot winner as they have exceeded their quota of foreign players. Turkish clubs are not allowed more than 10 foreign players every season.
At the moment, Fenerbahce have 11.