Five advice centres have secured funding to ward off the threat of closure.
Citizens Advice Scotland (CAS) said the offices in Glasgow will remain open for the next three years.
It follows changes to contract arrangements which pitted the service against a rival consortium, Glasgow Advice Agency.
The city council had put its advice contracts out to tender last year in four lots, with the total split between the two groups.
The authority said the intention was to allow smooth transition of services through subcontracts with no need for redundancies.
But on Monday CAS said a lack of detail in the arrangements would force the closure of its bureaux in Easterhouse, Pollok, Castlemilk, Parkhead and Bridgeton.
Susan McPhee, CAS acting chief executive, said a new offer has been agreed.
She said: "I am delighted to announce today that the boards of all five bureaux have agreed in principle to accept this new offer, and that as a result they will be able to remain open for the next three years
"This is excellent news for the people of Glasgow, who will continue to have a Citizens Advice Bureau service offering free, impartial, confidential advice."