Hitzlsperger, 30, was without a club after leaving Wolfsburg in the summer and thus able to sign ahead of the weekend's free transfer deadline.
He had been training with Everton since late September but will only feature against QPR if he receives international registration in time.
The deal runs until January.
The former Aston Villa, Stuttgart, Lazio and West Ham star has 52 caps for the German national team, the last of which was won two years ago.
Known for his powerful left-foot shot, 'Der Hammer' has been signed as cover for the injured Marouane Fellaini, who has been ruled out for up to three weeks with a knee injury.