Unison said it had secured “major improvements on pay and grading”.
It also confirmed that a proposal for pay protection for workers facing losses had been increased to three years.
The council has also agreed to continue discussions with the union on outstanding issues including lower-paid workers, allowances, unevaluated jobs, equality impacts and the operation of the new pay model.
Unison said the breakthrough created a route towards a ballot of its membership, without the council dictating the union’s recommendation or communications.
The union added that important issues remained unresolved but negotiations would continue before members voted.
Chris Sermanni, Glasgow City Unison branch secretary, said: “Unison stood firm because Glasgow’s workers deserved better than what was originally put on the table.
“That position has secured significant movement.
“There’s now a path for Unison members to give their verdict without the immediate threat of dismissal and re-engagement hanging over them.”