The Norwegian Under-21 international penned a new two-year contract with City recently and now he will look to gain valuable first-team experience in Holland.
Elabdellaoui follows in the footsteps of team-mate John Guidetti, who recommended his former Academy colleague to the Dutch side.
Guidetti spent a successful season with Feyenoord last season and proved to be a huge hit with the Dutch supporters during his stay.
“I spoke to John about the move and he had only good things to say about Feyenoord,” said Omar.
“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.”
