A section of the track by Trafford Bar was 30 years old and was torn out and replaced as part of the work.
Transport bosses say the repairs mean the tracks will not need replacing for another 30 years and passengers should see direct benefits once the lines reopen.
In one section of track being replaced, trams were previously limited to speeds of 5mph, but this could go up to as much as 20mph once the new tracks are in, making it less likely that services will face delays.
The new tracks have a different design to the old ones, and this is expected to make tram journeys feel smoother for passengers than they were before.