The building is due to become vacant when pupils and staff make the much-delayed move to their new school in February next year.
Councillors agreed in May 2015 to sell the current building to Cala for £14.5m – but the deal depended on planning permission for Cala’s development of the site.
And earlier this year the council’s own planning committee refused proposals for conversion of the main school building to 87 residential units, with eight affordable homes in the annexe and a further 20 affordable units in a new six-storey tenement on the site.
Cala lost an appeal against the decision but has now put in a new application for a reduced development.
And it has made a revised offer of a guaranteed minimum of £11.7m, which the council’s finance committee voted to accept – despite calls to pause the sale.
Liberal Democrat councillor Neil Ross said: “This set of circumstances presents us with an opportunity to step back and review where we are with school provision in the south of Edinburgh.”
Both the new Boroughmuir and the recently-opened James Gillespie’s High School are too small to cope with rising pupil numbers.
Cllr Ross asked: “Is there a potential use for the old Boroughmuir High School building?”
And Green finance spokesman Gavin Corbett said a delay in accepting Cala’s revised offer would also allow fresh exploration of a rival bid, rejected in 2015, from community group Out of the Blue, which wanted to turn the school into an arts space featuring studios, performance areas and workshops.
But officials told the committee the price difference – Out of the Blue offered £6.2m – was crucial in choosing the Cala bid. They said £7m of the sale money had already been used.
And they said refurbishing an old building cost more than building new accommodation.
Tory economy spokesman John McLellan said: “To defer in order to open up an opportunity for the council to take less money for a site where it has already spent the money seems to me an absolutely profligate way of looking at the public finances.”
Local Green councillor Melanie Main said she hoped it would not be a decision the council came to regret.
It emerged last month that the opening of the new Boroughmuir High School has been met with a fresh delay after it was announced pupils would not now move in until February.
Students had been earmarked to settle into their new classrooms in January but will now not move in until the latter half of the following month.
The move, which follows consultation with the headteacher and wider school community, will see the new school fully operational immediately after the February mid-term break.