This opens up many more of the islands for travellers.
Brown said the decision was taken after discussion with the Pa Enua mayors of the outer Cook Islands and Health Ministry Te Marae Ora.
"The removal of these final restrictions means that, as a country, we are sending a signal to the world that we are serious about getting back to business and we want our people to live normal lives without unnecessary government restrictions."
The Cook Islands Tourism industry also welcomed the news, which removed the final travel restrictions of a long and difficult pandemic.
GM of the Cook Islands TC for New Zealand and Australia, Graeme West said it represented a return to "normality" just in time for additional flights returning from late October.
"Rarotonga and Aitutaki are looking stunning, and Cook Islanders are waiting with their usual warm welcome for all our visitors."