Perth and Kinross councillors have agreed a £5.2 million commitment for the extension at Dundee's Harris Academy to proceed.
It means Invergowrie secondary-aged pupils can continue to be taught two miles away in Dundee rather than being bussed 22 miles to Perth High School.
Costs for the project - which is expected to be signed off by both councils in December 2022 - are estimated to have spiralled by a further £1 million.
Councillors on Perth and Kinross Council's Finance and Resources Committee gave their approval when they met on Wednesday, November 30.
Councillors agreed to increase the budget for the Dundee City Council school's extension project from £4.2 million to £5.2 million by drawing from PKC's additional borrowing capacity built into its approved Capital Funding Strategy.
At Wednesday's meeting Liberal Democrat councillor Peter Barrett sought assurance "all efforts are being made to minimise these costs" and there was "full transparency on the costs available to the council".
PKC's head of Business and Resources Greg Borland said: "We have a joint project board with Dundee City Council. All information is scrutinised by head of Property[Services] Stephen Crawford.
"So we're quality assuring it, making sure we're comfortable and we're at the point - subject to agreement today - of signing the contract with Dundee City Council for the extension to proceed."
The committee's convener SNP Strathearn councillor Stewart Donaldson said: "I welcome that we expect to achieve financial close on Harris Academy very soon indeed."
Learning and Families convener John Rebbeck said it felt "like a very sensible solution".
The SNP councillor added: "I don't think we want to be explaining to parents in Invergowrie why we're bussing their kids all the way up to the [Perth] High School when there was another option available."
Local Carse of Gowrie councillor Angus Forbes agreed.
The Conservative councillor said: "I'm pleased to see this progress and I certainly couldn't look the parents of children in Invergowrie in the eye and tell them this wasn't going ahead. So - thankfully - I'm not going to have to do that."
The 640m² extension at the rear (south side) will provide five additional classrooms, a drama studio, offices, a plant room and a break-out space.
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