The central midfielder has been training with the club for several weeks and featured in the u21's 2-0 victory against Norwich City prior to the international break.
Hitzlsperger has already played for Aston Villa and West Ham United in the Premier League, but has suffered from consistent injury problems in the past three years and never returned to the form he had in five seasons at VFB Stuttgart, where he anchored the midfield and earned himself a regular place in the German national team.
Last season, after featuring only six times for Wolfsburg, the 30-year-old's contract was terminated and David Moyes decided to bring him in this fall on a similar deal as ex-Scottish international James McFadden last year.
Hitzlsperger will serve as veteran cover for Darron Gibson and Marouane Fellaini in central midfield following the sale of Jack Rodwell in August.
Following the official presentation last night, Moyes stated to the press:
This two months where we have him on a short contract means we can have a longer look and get him involved when we can and where we need to to see a bit more. I think January would be a better time for us to decide whether we were going to continue his contract until the end of the season or extend it even longer.
Hitzlsperger will wear the No. 16 jersey last donned by Jermaine Beckford before his move to Leicester City at the beginning of the 2011-12 season.