The space is currently being used for archives and storage, which will be moved to council's off-site storage.
Napier Mayor Bill Dalton said this was an exciting move, which would have benefits for all, and had received widespread support.
"It's a great solution to what has been a perplexing issue for us all, and one I'm fully in support of.
"Having the library at MTG Hawke's Bay also has the bonus of bringing a larger number of our community, who might not have experienced the MTG before, into this wonderful building."
Yesterday the council's finance committee also approved a statement of proposal, which explored options for the future use of the two civic buildings.
Council chief executive Wayne Jack said it had been found council administrative services and the library could fit into one building.
So, council needed to decide if it would renovate, or rebuild using both buildings, or just one.
The proposal - which will go out for consultation - suggests the council could divest the site currently occupied by the administration building, either by sale or long-term lease, to a private developer for commercial development.
A feasibility study found the commercial use which would best benefit the city would be a hotel - rather than retail, or office accommodation. This idea was revealed by Hawke's Bay Today in March.
If progressed, the council and library could be located in the other building - currently occupied by the library.
Mr Jack said this approach would bring several benefits to Napier.
"Economic growth for one, as well as rejuvenation of the CBD area, increased foot traffic and improved public spaces, a number of jobs, and the opportunity for a developer to create something visually and architecturally appealing here on Hastings St."
Going forward, the council were also developing a library strategy which would inform any decisions on a permanent home for the library.
At least four possible sites had been identified, council director city strategy Richard Munekke said. These included the current library building (once redeveloped), the Vautier St carpark, Ocean Boulevard/carparking building, or a library which would join Clive and Memorial squares.
All three leases have now been signed on the buildings to be occupied by council's civic administration staff with all teams expected to have relocated by Christmas.
The final to be confirmed is Dunvegan House, where antique store Finders Keepers is currently, and where a full customer services counter is planned.
• Submissions on the council's statement of proposal open on October 4, and close on November 3.