"Tenants of council-owned buildings will be expected [to] adhere to the policy," the report says.
Public feedback on the draft policy will be sought throughout July.
The consultation process will include an online survey, a written submission form and direct consultation with retailers and hospitality businesses via a workshop.
Council staff will collate and summarise the feedback received during the month, and develop a final policy and implementation plan during August.
The final policy will be presented to the the two councils for approval in September ahead of an implementation plan being initiated in October.
The Napier City Council staff report said the main cost of the policy would be in consultation costs (which are accounted for in existing budgets), signage and installation.
"New signage can be installed in phases, with priority areas being completed first," the report said.
The joint council proposal is supported by the Hawke's Bay District Health Board.
A recent survey commissioned by the DHB showed strong support for public areas being smoke free.
The planned policy builds on the smoke-free sports grounds and playgrounds policy Napier adopted in 2008.