She was 20-year-old Ashwini Rasiwala from France. Police said she was found dead in the river on Saturday, February 8.
The other trampers who died in the vicinity this month were were Kevin Kum Fike Lee (22), who resided in Dunedin, and Briton Stephanie Simpson (32). Their bodies have also been found.
The bodies of Ms Rasiwala and Mr Lee were found within a day of each other, in the same area, and police said at the time they thought the pair may have been tramping together.
The deaths all came after several days of extreme weather in the lower half of the South Island.