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.
He said: "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.
"The unions remain divided and the time has come to apply the deal."
The agreement does not include teachers. Members of the Educational Institute of Scotland teaching union rejected changes to their working conditions this week.