The Norway Under-21 international has yet to make an appearance for City's first team but was an unused substitute in December 2010's Europa League group game against Juventus.
He follows in the footsteps of team-mate
"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," Elabdellaoui said.
Elabdellaoui signed a new two-year contract with City earlier this year.
English Premier League
Aston Villa boss Paul Lambert has warned Christian Benteke he faces a "reality check" after reports suggesting the striker could be keen to leave the club.