More extensive investigations were carried out on the building earlier this year to assess the extent of the damage and appropriate repair options.
But the process was hampered by the discovery of new cracks in the floors, meaning additional propping had to be installed to ensure the safety of those working inside the building.
Foster said this agreement, along with the recent decision to strengthen the central library, meant the council could start talking with the community about the future of Civic Square.
"It will be a chance to think laterally and creatively, and collectively this will be an exciting opportunity for Wellington. I look forward to talking more about this very soon."
Council Chief Financial Officer Sara Hay said senior council staff, engineers and insurers have all been involved in the drawn out negotiations over CAB.
"This centred on the question of how badly damaged the building actually was and the question of whether it should be repaired or demolished."
A decision on the future of CAB is yet to be made.
Council Chief Executive Barbara McKerrow said it would be an important consideration in relation to decisions about the future of the adjoining Municipal Office Building (MOB) and the Civic Precinct as a whole.
Last month the Herald revealed the cost to redevelop MOB, a key building in Wellington's national music centre plans, has blown out to $84 million - more than double the initial estimate.
Foster and councillors are scheduled to receive a report on MOB and related issues before Christmas.
Council staff used to have their offices in CAB but were turfed out after the 2016 earthquake and moved to MOB and other buildings around the city.
But noisy earthquake remediation work on the neighbouring Town Hall meant they had to move out of MOB too.
They started the move to their current premises on 113 The Terrace at the end of 2018.
It's costing the council more than $3.6 million in rent for every year it's unable to return to its offices in Civic Square.
