General union GMB said the deal could be worth up to 20% for lower paid workers on the contract where skilled workers were bizarrely getting paid less than labourers.
GMB, Unite and Ucatt have been in dispute for nearly two years with Sheffield City Council over pay differentials between craft workers and employees graded as labourers.
Pay for labourers was subject to a job evaluation process in 2010 after which their pay increased.
But craft workers were left out of the job evaluation process resulting in them receiving lower pay than labourers.
The pay anomaly led to strike threats and in August this year workers transferred from the council to Amey under a massive PFI deal.
Peter Davies, GMB organiser, said: “Unfortunately the Council were not willing to settle this dispute despite our threat of strike action.
“This was partly because they knew that the vast majority of craft workers were due to transfer from the Council to Amey last August and partly because they claimed they did not have money to afford this pay rise.”
The union said Amey has been keen from “day one” to resolve the dispute.
Davies said: “This sounds like a huge rise in this day and age but what this really shows is how far public sector craft workers have fallen behind in terms when it comes to a fair days pay for a fair days work.
“These craft workers can now concentrate on the job of delivering what Sheffield needs, great roads, street lighting and top notch pavements.
“Now we need to pursue a similar deal for the craft workers that remain employed by the council.”