Unison said its lawyers will now enter legal discussions over the financial settlement of members’ equal pay claims.
Further strike action was planned for April 20 and 21 and for May – however, Unison and GMB said these are now suspended.
Glasgow City Council agreed to pay out at least £500 million in 2019 following a long-running equal pay row.
In a letter to its members on Wednesday, Unison Glasgow City Branch said: “The industrial dispute objectives were to force the council to maintain the 2019 deal and agree to make further payments in an acceptable timescale.
“These objectives have been secured. As stated previously, these were only won because trade union members were prepared to take strike action. Well done again to all Unison members and to our sister trade unions.”
The union said the Unison strike ballot remains “live” under current UK law and stated that it will be “closely monitoring the progress to deliver further payments as agreed by the leader of the council”.
Unison’s Scottish secretary Tracey Dalling said: “It is simply unacceptable that women were forced to take their fight all the way to the brink of strike action.
“However we now seem to have reached agreement. There is still hard work to do, but this is good news for everyone across Glasgow.”
Sean Baillie, GMB Scotland Organiser, said: “For GMB members in Glasgow City Council, equal pay justice is a significant step closer.
“The incredible strength and solidarity of GMB members, throughout many years of struggle, has been critical to achieving this progress and securing key commitments from the council.
“We will monitor developments closely, as further details of the implementation of these commitments emerge, and our mandate for strike action remains live.”
The 2019 agreement settled pay claims up until March 2018 and included a new pay and grading system to rectify issues of unequal pay, primarily for women.
Unison said that, since then, around 5,500 new claims have been lodged for the period prior to March 2018, with nearly 20,000 claimants awaiting settlements for the period after that.
In a letter to trade unions, Glasgow City Council leader Susan Aitken said the local authority remains “committed to a settlement which has the same basis as the 2019 deal”.
She said: “We continue to work towards getting a financial package secured which would allow for a deal on the same basis to be agreed.
“The Council is also prepared to consider an interim or phased payment, subject to negotiation, if that was agreeable to all parties. We are also targeting a payment by October.”
A Glasgow City Council spokesman said: “The council is committed to delivering pay equality and is pleased the planned industrial action has been suspended.
“We will continue to work with trades unions and others representing claimants to deliver a settlement.
“Families and citizens who have previously been contacted about school and nursery closures or other disruption can now expect normal services to be in place.”