Foster carers working directly for Liverpool City Council will no longer have to pay council tax.
It will mean a saving of at least £1,100 per year for the 290 households who currently foster one or more child.
The council estimates the scheme, part of a drive to encourage more people to become foster carers, will cost around £372,000 to fund in 2016/17.
But it says the move will save £500,000 if it leads to the recruitment of 10 additional foster carers to replace high-cost residential homes and agencies.
Liverpool has at least 150 more looked-after children than it had five years ago, with a current total of about 1,000.
The council says the rise is reflected across the country and is due to a greater level of awareness of child neglect and abuse following the Baby Peter case in Haringey.
Liverpool mayor Joe Anderson said: 'This is our way of saying thank you to our foster carers and recognising the amazing work that they do to protect and support some of the city's most vulnerable young people.
'We really need more foster carers to come forward and work for us, and I believe this scheme will encourage families who want to foster but are worried about the costs that come with looking after a young person.'