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.