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 John Guidetti, who made a similar move last summer and enjoyed a prolific season in Holland.
"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.
Source: PA
Source: PA