Council tax bills in England are set to go up by an average of 3.9% - the lowest rise for 14 years, says the public accountancy institute, Cipfa.
The average bill in England will go up by £52 a year
Cipfa's survey for BBC Radio 4's Today programme and the Times newspaper showed average bills for a Band D home will go up by £52 a year to £1,370.
The government had said it wanted council tax rises substantially below 5% - and most councils complied.
Wakefield, Derby, Leicester and Slough face the steepest rises at around 5%.
Much of the rise in council tax bills is due to sharp increases in the costs of policing, including the employment of more Community Support Officers.
In Lincolnshire the police precept has soared by 79%, adding £100 to the average council tax bill.
But the BBC's local government correspondent John Andrew said the government would be pleased that its policy of capping council tax rises had been largely successful.
He said councils had been motivated by capping and by local political pressure into becoming much more efficient, but the government was seeking greater economies in the future.
Local Government Minister John Healey said there was no excuse for excessive council tax increases. He said the government would continue to use its capping powers to protect the public.
"By cutting waste, councils could save as much as £1.5bn, which could be used to invest in local services or reduce pressure on council tax bills", Mr Healey said.
Central government funding for local authorities will increase by £900m. Mr Healey called this "a fair and affordable settlement" which had helped keep council tax bills down.
But the Local Government Association criticised the government grant settlement as the worst for 10 years, and warned it could lead to cuts in local services.
"Keeping council tax down has been made harder by several government departments shifting extra costs on to councils, whilst limiting funding from central government to a real terms 1% increase", LGA Chairman Sir Simon Milton said.
He said the there would be "difficult decisions to make locally."
The National Pensioners Convention said that even at below 5%, this year's council tax bills would still "bring more misery to millions of pensioners".
General Secretary Joe Harris said the average Band D bill of £1,374 represented about a third of pensioners' spending, and came on top of rising food and fuel bills.
"The government has no solution to the unfairness of council tax, apart from asking pensioners to claim discredited means-tested benefits", Mr Harris said.
"We urgently need complete reform of the system that takes account of the ability to pay."
The Conservative Party agreed that the problem for council tax payers was the combination of increased bills with rising gas, water and electricity costs.
Shadow local government secretary Eric Pickles said it would be the most vulnerable who would suffer the most, including the elderly and other people on fixed incomes.
"It is shocking that council tax has doubled in 10 years of this Labour government", Mr Pickles said.