Police have not identified the woman but she has been named in Sydney media as Yessica Asmin, from Indonesia, who is an international student at the University of NSW.
Rescuers found her body on Wednesday, two days after she was swept away while hiking on the Milford Track in the South Island.
She had been walking on the track with her boyfriend Sean McNabb, who is from Sydney, and German backpacker Sebastian Keiholz, Fairfax Media reports.
The two men managed to cross the stream but Ms Asmin got caught on a rock in the middle and panicked and fell. She was swept away.
Mr McNabb paid tribute to Ms Asmin on Facebook.
“Thank you all for your love and support,” he posted, according to Fairfax.
“Yessica was fond [sic] today deceased. Today I lost a part of me, I’m very lost at this time.”
Ms Asmin’s family have arrived in New Zealand and are being supported by police.
She was walking the track, when she was overwhelmed by the water in Pompolona Creek and swept into the Clinton River late on Monday.
A search by a helicopter on Tuesday failed to find any sign of her.
The Clinton River normally flowed at a level of 0.25m but was flowing at 1.8m on Wednesday, having been at 2.2m on Tuesday night.
Mr Keiholz activated an emergency locator beacon and ran to the nearest hut.