"The Fiordland and the Wakatipu communities have had a difficult year.
"Having these tracks reopened not only encourages people to connect with nature, but encourages visitors back into this incredible part of the country."
The Routeburn was among 78 tracks in the Fiordland and Mount Aspiring National Parks damaged in the storm.
Lake Howden Hut, which was hit by a landslip on February 4, was so badly damaged it was deemed unsafe and closed immediately.
It was demolished and its materials flown from the site by helicopter last month.
The statement said contractors had been working on the track since September, repairing the damage from landslips and reinstating the track.
Five new bridges had been built between Lake Howden and Lake Mackenzie Hut.
Bookings for the track were strong, with the holiday period "almost at capacity".