The decision was made by the Cabinet committee today, she said.
The refugee quota became an issue of contention recently after conflicting comments from Peters and Ardern on whether it would be raised.
But Peters said he supported today's decision.
Ardern said the 2020 timing meant that preparations could be made to ensure refugees were well-supported when they arrived.
"I'm proud that the coalition Government has today agreed to make such a significant and historic increase to the annual quota of refugees," Ardern said.
"This is the right thing to do. It fulfils New Zealand's obligation to do our bit and provide a small number of people, displaced by war and disaster each year, a place to call home."
Ardern said the policy shift would "change lives".
"Refugees become great citizens, who bring valuable skills and experience to New Zealand and help make our country a more diverse and vibrant place."
Peters told reporters while in Nauru recently that New Zealand First had never made a commitment to double the refugee quota.
NZ First had agreed to increase the quota to 1000 but had made no announcement to double it.
"We've got 50,000 people who are homeless back home, and I can show you parts of the Hokianga and elsewhere, parts of Northland, with people living in degradation," Peters said.
"We have to fix their lives up as well before we start taking on new obligations of the level that some people would like."
For 30 years New Zealand's refugee quota was 750 people per year.
The previous National government increased the quota to 1000 in 2016, which took effect on July 1 this year.
Labour campaigned before the election on increasing that further to 1500 a year in its first term of government.
Budget 2018 provided $6.2 million of new operating funding over the next four years, plus $7.7 million of new capital, for two new accommodation blocks at the Mangere Refugee Resettlement Centre.
An extra six settlement locations would be needed nationwide on top of the eight already in operation, Lees-Galloway said.
The Government will also fund the expansion of public housing for around 150 extra refugee families at an estimated total cost of $32.5 million over three years.
