Council umbrella body Cosla said employees will see a 1% rise for 2013-14, backdated to April 1 and a further 1% increase from April 1 next year.
Human resources spokesman Billy Hendry said Cosla could not allow the "dragging of feet" by Unison to continue.
"We have been in negotiations with the Scottish Joint Council trade unions for almost a full year after making an initial offer in November 2012," said Mr Hendry.
"The unions remain divided and the time has come to apply the deal."
The agreement does not include teachers. Members of Scotland's largest teaching union, EIS, rejected proposed changes to their working conditions this week.
Mr Hendry said: "It is deeply frustrating for me that I am not in a position to announce a pay increase at this time for our teaching workforce. The decision by the EIS not to agree a deal has resulted in what we believe is an unnecessary delay.
"Talks will continue in November which we hope will also bring this matter to a conclusion."