A £180,900 grant to begin work to restore the Harris was taken on board by councillors at Preston City Council.
The authority found out it was successful in winning the money for the museum and art gallery from the Heritage Lottery Fund (HLF) in January.
Putting forward the motion to formally accept the funds at a meeting on Thursday, cabinet member for Resources and Performance, Coun Martyn Rawlinson said: “This is just about accepting the grant funding.
“This is to put much more detail on the scheme. Once you get the first choice you usually get the rest but there’s a lot more work to do.
“Without this vision the Harris could well be a much reduced operation with austerity.
“This is absolutely fantastic news and the team has done incredibly well.
“We really need to deliver this for the future of that building and for the future of arts and culture in Preston.”
Welcoming the motion coun Lona Smith said: “We were all anxious that the Harris should do well.”
A part of the motion councillors were also asked to vote through a further £525,870 from the city council's own monies and from Lancashire County Council to support the project.
Winning the initial HLF grant has been three years in the making and means staff at the Harris are at liberty to undertake preparatory work and flesh out more plans to revitalise the building as the cultural hub it was build to be.
A second round of funding is now to play for for the £10.02m cash.