The pound;136 million programme, increased from an initial pound;70m, was agreed by the council's policy and resources committee on Tuesday for submission to the Scottish Office.
Glasgow's proposed PFI scheme, renamed public-private partnerships (PPP) under New Labour, will now swallow a third of the Scottish Office's pound;400 million ceiling for such schemes.
The project will compete for Government approval against a wide range of educational and non-educational bids.
Frank McAveety, the city's Labour leader, described the project as "a trail blazing programme which will put Glasgow at the forefront of raising secondary school standards in the UK".
The committee approved the plan by 13 votes to 3. An unlikely alliance of Chris Mason, the Liberal Democrat leader, Kenny Gibson, leader of the SNP group, and Tommy Sheridan of the Scottish Socialist Alliance, opposed it as "privatisation by the front door".
But the council's Labour administration insists the PPP route is the only way of injecting funds quickly into the school system. It admits, however, that completion of the refurbishment programme by 2001 is "a very tight timescale". The conventional route through borrowing capital on the open market would take until 2014.
The PPP route means the money will be invested by a consortium from the private sector and the buildings leased back to the council for 30 years. The successful private bidder will bear the full maintenance and repair costs, and will be able to bring in income from other activities when the schools are not in educational use.
The council aims to have the contracts signed by next June. The Scottish Office will be expected to provide annual support of pound;17m.
Under the deal teachers and administrative staff will continue to be employed by the education authority. But non-teaching staff - including up to 500 janitors, cleaners and technicians - will be transferred to the private sector. Their unions are furious, but the council has pledged to protect their conditions in negotiation with the private consortium.
The pound;136 million will be used to refurbish 27 secondaries, build two new secondaries, one new primary and seven major extensions and upgrade IT facilities in all the schools.
The programme, designed to restore Glasgow's battered educational image, has involved the closure of seven secondaries. Another two are scheduled to go following public consultations launched this week.
This will release a total of pound;8m by 2002, which the council has promised to reinvest in school staffing and resources.