The carpark area is generally under-used, the council said in a statement.
The statement said the decision aligned with the council's Rotorua 2030 vision and goals, which included key strategies for creative communities and inner city revitalisation.
It also fits well with its master plan for revitalisation and development of the Kuirau Park area, and would provide a link with nearby Parksyde, Rotorua's community centre for senior citizens, it said.
The council has been working with the Rotorua Continuing Care Trust to help find a new location for the home and hospital.
Councillor Mark Gould, spokesman for the older persons' strand of the council's Rotorua 2030 People Strategy, said this was an exciting and important opportunity for Rotorua.
"Whare Aroha CARE is a community centre which requires a modern pleasant building and with the increasing of the 55-plus population, these services will be much needed for Rotorua residents in the future," he said.
"The area around Kuirau Park is ideal with plenty of green and open space for guests and their families to enjoy the environment, while creating more activity in this central but under-utilised area close to the CBD."
The council had previously supported relocating the facility to the Rawhiti pensioner housing complex in Glenholme.
However, further investigation found that would not provide enough space.
Following Thursday night's approval in principle, the proposed relocation will now be included in the 2014/15 draft Annual Plan for public consultation.
The proposal would involve no cost to the council with the trust responsible for the cost of creating replacement car parking at the Aquatic Centre.
Council staff have suggested that should be located towards the centre of Kuirau Park, providing centralised parking for all park users and fitting with plans for the Aquatic Centre to open out on to the park in the future.
A review of council reserves and land concluded the Kuirau Park site was the only one large enough for Whare Aroha CARE and offered the most value for the community.
Subject to discussions with the Bay of Plenty Regional Council the facility may also have access to geothermal energy for heating, the statement said.