Elabdellaoui has signed on-loan for the season with the Dutch.
"I spoke to John about the move and he had only good things to say about Feyenoord," he told City's website.
"It's an exciting challenge for me and it gives me the opportunity to play regular first-team football that will obviously benefit me and hopefully City as well in the long-term.
"I was very happy to agree a new contract with City so everything is moving in the right direction. I'm just going to do my best for Feyenoord and enjoy my time in the Eredivisie."