A settlement which could reach up to £600,000 has been agreed, though Ms Shoesmith may receive a lower sum, according to BBC2’s Newsnight.
Some of the cash will come from central government coffers but Haringey council, in north London, will foot most of the bill, it reported.
Mr Balls removed Ms Shoesmith from her £133,000-a-year post as Haringey Council’s director of children’s services after a damning report on the death of Peter Connolly.
She was then fired by the council without compensation in December 2008, after a report from regulator Ofsted exposed that her department failed to protect 17-month-old Peter – then known publicly as Baby P. She has reportedly not worked since.
Mr Balls, now Shadow Chancellor, said: “An independent report said there were disastrous failings in Haringey children’s services.
“They said the management was at fault. Sharon Shoesmith was the director of children’s services and so of course it leaves a bad taste in the mouth that the person who was leading that department and responsible ends up walking away with, it seems, a large amount of money.”
Downing Street said the Department for Education’s contribution would be made public.
At a regular Westminster briefing the Prime Minister’s official spokesman said: “With regard to the amounts, that’s a legal agreement between Ms Shoesmith and Haringey so I don’t propose to comment on that.
“With regard to confidentiality clauses, that’s again one that has been agreed between the council and Ms Shoesmith. It would be for the council to justify that.
“As part of the Court of Appeal ruling the Department for Education was ordered to pay a contribution to her payout.
“Whilst that contribution hasn’t been agreed the Department for Education will make public the amount that it is contributing.”
The Morley and Outwood MP said: “The payout is something that will appal people across the country. What it can’t do is bring back a little boy who lost his life because he was failed by Sharon Shoesmith and that department. That’s the truth and that will never change.”
Ms Shoesmith’s lawyers argued that she was the victim of “a flagrant breach of natural justice” fuelled by a media witch-hunt.
In May 2011, the Appeal Court concluded she was unfairly sacked because Mr Balls and Haringey did not give her a proper chance to put her case.
The Department for Education and Haringey sought permission to attempt to overturn the ruling in the Supreme Court, but judges rejected the applications, clearing the way for her to receive compensation, which some experts predicted could be in the region of £1m.