Susan Aitken, the leader of Glasgow City Council, confirmed the authority has “agreed an offer” with the organisations representing the thousands of workers affected.
The council stressed, however, that the agreement is not the end of the process and a number of steps need to be taken before payments can be made.
Ms Aitken said: “After a decade of obstruction and inaction, in a relatively short space of time we have now reached agreement which delivers the pay justice these women long have fought for.”
She said she is “proud to be able to recommend a settlement to right this historic injustice”.
Ms Aitken had pledged to settle the historic dispute when she became the first SNP leader of the council in 2016.
She added: “It’s been a difficult journey but I have never once hesitated in my commitment to deliver pay justice in Glasgow.”
The agreement in principle comes after some 8,000 Glasgow council workers walked out on strike for 48 hours in October last year in a bid to settle the pay claim.
Around 12,500 workers, mostly women, were proceeding with claims against the council following a Court of Session ruling in 2017 that female workers had been discriminated against.
The council adopted the Workforce Pay and Benefit Review (WPBR), implementing its job evaluation-based pay and grading system in 2006 with the aim of ensuring men and women received equal pay for jobs of the same value.
However, some women claim they were paid £3 an hour less than men in similarly graded roles.
Council bosses said at the time of the October strikes that such action was unnecessary, and they hoped to reach a settlement in the following months.
Stefan Cross QC from Action4equality, which represented some of the claimants, said. “Since the strike there has been real and constructive negotiations.
“Neither side has got everything it wanted and both sides have made serious concessions so that we can both be satisfied that this is a fair deal.”
Before the payments can be made, the deal has to be approved by members of Glasgow City Council.
The authority is also “completing the process” of raising the necessary funding to cover the cost of the payments.
Wendy Dunsmore, regional industrial officer for the Unite union, hailed it as a “day of celebration for the workers in Glasgow City Council who were unfairly treated and discriminated against”.
She said: “These workers have been financially disadvantaged for years. The deal addresses these historic wrongs. Unite members will be delighted that the many years of wait is almost at an end.”
GMB Scotland organiser Hazel Nolan said: “This is a significant moment and is recognition of the value of women in this city, brought about by the women themselves understanding their own value and fighting for it together.
“What is important now is that the claimants and their families can have confidence in this agreement and in the process of delivery in the coming weeks and months.”