The Sarjeant Gallery Trust has raised 90 per cent of the required money.
Just over $400,000 of the bequest sits in two funds while the remainder exists as a 10 per cent share of property on St Hill St.
That will be sold to the harbour endowment - a portfolio of 97 commercial properties - managed by the council.
"[It] generates some income which has gone to the Sarjeant over the years for its acquisitions fund," said council libraries and community manager Pete Gray.
"One of the reasons there is so much money in this fund at the moment is that the gallery has not been spending the money from the acquisition fund."
In a report to councillors Mr Gray said "this use of the remaining bequest funds is entirely in line with the terms of the original bequest but requires a positive decision by council as the trustee of the funds".