Services will resume between Wolverhampton and Bull Street, with trams running up to every 10 minutes.
At the time West Midlands Metro said it would be at least four weeks before enough trams were available to sustain a "safe, reliable and robust service."
The company said comprehensive safety checks have been carried out on all vehicles as part of the repair process.
Engineers are said to be working "tirelessly" on the repairs and trams are being put back into service as they become available.
This week a number of new trams are also being tested and will later be introduced to the tracks.
As more trams are repaired and more join the fleet, the service will be extended to the Library of Birmingham at the "earliest opportunity".
West Midlands Metro Service has again apologised for the disruption and says "the safety of our colleagues and customers remains priority".
The company said it continues to "focus on delivering a safe and secure, reliable and sustainable service."