Councils have saved£3.45bn in that period, the equivalent of£129 off the average Band D council tax bill, according to Mr Healey.
He said: “Councils should be praised for making efficiency savings that have exceeded expectations. This is an excellent achievement and one that will stand them in good stead in this global economic downturn.
“Over the next three years, I will be looking to councils to make nearly£5bn efficiency savings. This is in the interest of local authorities, who can use these savings to cut council tax bills or invest in local services."
Top performers included Manchester City Council and Birmingham City Council, who saved£53.7m and£84.8m respectively.
The announcement came hot on the heels of shadow chancellor George Osborne pledging a two-year freeze on council tax during his address at the Conservative party conference this week.
This would be funded by slashing£500m off the bill for consultants and advertising in their first full year of government, and by£1bn in all subsequent years, Mr Osborne claimed.