The 28-year-old joined the Spanish side from Valencia in 2010, scoring 12 times in 38 league appearances in the 2011-12 campaign.
But he has since struggled to force his way into the first team and was loaned to Celtic last season, where he played 11 Scottish Premiership matches, finding the back of the net twice.
Miku started three of Getafe's La Liga games this season, scoring twice against Osasuna earlier this month.
But the Madrid-based club have revealed he is moving to Qatar.
"Getafe CF, SAD and Al Gharafa Sports Club have reached an agreement for the transfer of the player Nicolas Fedor, 'Miku'," a statement on Getafe's official website read.
Arthur Coimbra's Al Gharafa currently sit tenth in the Stars League after three games, picking up draws in all of their opening encounters.
