Matches will be played at the 5,000-capacity Waitakere Stadium in Auckland and the Northland Events Centre in Whangarei, as well as the 25,000 capacity Albany Stadium and Eden Park, which hosted the men's Rugby World Cup 2011 final.
New Zealand Rugby chief executive Steve Tew and board members Farah Palmer and Mark Robinson faced a World Rugby panel in Dublin to support the bid. The panel voted 25-17 in New Zealand's favour.
"Congratulations to New Zealand on being elected women's Rugby World Cup 2021 host," World Rugby chair Bill Beaumont said in a statement.
"They presented a very strong and compelling bid and we look forward to working with New Zealand Rugby to host a successful and inspiring tournament.
"I would also like to thank Australia for their exceptional bid. We hope to welcome Australia back to bid again in the future."
New Zealand prime minister Jacinda Ardern said it was a proud moment for the country as her government seeks to promote women's sport.
"I'm hugely excited the event will be held here," she said.
"This government is committed to more women and girls getting involved in sport, so we are enthusiastic supporters of bringing this elite women's tournament to New Zealand and inspiring a new generation of women and girls to get involved in rugby."
New Zealand won a record fifth women's Rugby World Cup title last year in Ireland, beating England 41-32 in the final.
(Reporting by Hardik Vyas in Bengaluru; Editing by Christian Radnedge)
