Cabinet ministers have this afternoon signed off on a 17 May start date, pending final confirmation by New Zealand's Director-General of Health and the Cook Islands Secretary of Health.
It will be subject to final checks such as airline and airport preparedness.
New Zealand would be providing the Cook Islands with enough vaccine to immunise its population. That roll-out would also commence later this month but is not considered a pre-condition for the bubble.
"There is no vaccination under way in the Cooks," she said, but the population in Rarotonga was worth one day's vaccination in New Zealand.
As for travel between Australia, Cook Islands and New Zealand, she said at this stage, the Cook Islands were asking anyone travelling from Australia to go via New Zealand, but that could change.
"Having that triangular movement is something we are very open to."
There will be no requirement for a pre-departure Covid-19 test, but travellers will have to complete a travel declaration, provide a health declaration and there will be random health checks at airports.
No one should travel if they are unwell, if they are waiting on a Covid-19 test, or if they have been in contact with anyone suspected to have Covid-19.
Ardern said there were talks of about two or three flights a week from New Zealand to the Cooks this month, which would then scale up.
A huge amount of work had gone into ensuring the two-way bubble was safe and that the Cook Islands was set up and ready for it, she said.
"This is a world-leading arrangement and it's important to remember many other countries still have bans in place on travel for holiday purposes."
In a statement, Cook Islands Prime Minister Mark Brown said it was the start of a journey of recovery.
"Today we get back to business. Today with our joint confirmation of the 17 May, we give our people, and particularly our industry, the certainty necessary to institute remaining preparatory steps to once more welcome visitors to our shores."
The announcement has been a long time coming, after Ardern initially promised the arrangement would be in place by the end of March.
Cook Islanders have been able to fly into New Zealand without quarantine since January.
As for travel bubbles with other countries, Ardern said the government was looking at the realm countries first.
"For Niue, when they're ready, we're ready."
Covid-19 Response Minister Chris Hipkins said the government had a "brief" conversation around repatriation flights but no decisions were made yet.
He said flights were still not operating from India and "our decisions on repatriation will very much depend on how long those restrictions go on for".
"We'll review it each week."