Ardern arrived aboard an RNZAF Boeing 757 from Cyclone Gita-ravaged Tonga, after previously visiting Niue and Samoa.
She was greeted by Cook Islands prime minister Henry Puna and New Zealand High Commissioner Peter Marshall.
Traditional dancers also performed as part of the welcome for the delegation.
Today will be a busy one for the recently-appointed PM. She will start with a private breakfast with Puna, deputy prime minister Teariki Heather and finance minister Mark Brown.
From there she will head to the House of Ariki, before sitting in with cabinet at the Office of the Prime Minister
Following the cabinet meeting, local and New Zealand media will have the opportunity to ask questions of both Ardern and Puna at a press conference on the office lawn.
After travelling to Muri, she will enjoy a long lunch with Queen’s Representative Tom Marsters, after which she will get a chance to check out the lagoon on a local cruise.
Following a brief break, Ardern will take part in a “meet and greet” with the LGBTQI support group Te Tiare Association.
The night ends with an evening reception hosted by the Cook Islands Government at the National Auditorium.
Accompanying Ardern will be New Zealand deputy prime minister Winston Peters, who recently paid a visit to Rarotonga for the wedding of New Zealand MP Shane Jones.
Included in the delegation are New Zealand cabinet ministers and members of parliament, including the minister for Pacific People Aupito William Sio, minister for Climate Change James Shaw, as well as National MPs Gerry Brownlee and Alfred Ngaro.
Ngaro, a Cook Islander, and Brownlee were both present on last year’s Pacific Mission to the Cook Islands with former prime minister Bill English.
Members of New Zealand’s media, business community and non-government organisations are also in the delegation that will be on Rarotonga until Thursday.