In what Ed Balls, the children secretary, described as "stain on our society" the child migrant programmes saw poor, orphaned and illegitimate children sent to Australia, Canada and other former colonies until as recently as the late 1960s, often without the knowledge of their families.
Many ended up in institutions, many suffered abuse and neglect and many others were used as "slave labour" on farms.
Now after years of campaigning from pressure groups, Gordon Brown has agreed to meet with representatives of the surviving children before making a formal apology next year.
Mr Balls said the apology would be "symbolically very important".
"I think it is important that we say to the children who are now adults and older people and to their offspring that this is something that we look back on in shame," he said.
"It would never happen today. But I think it is right that as a society when we look back and see things which we now know were morally wrong, that we are willing to say we're sorry."
The government has estimated that a total of 150,000 British children may have been shipped abroad under a variety of programs that operated between the early 19th century and 1967.
A 2001 Australian report said that between 6,000 and 30,000 children from Britain and Malta, often taken from unmarried mothers or impoverished families, were sent alone to Australia as migrants during the 20th century.
Some of the children were told, wrongly, that they were orphans.
The migration was intended to stop the children being a burden on the British state while supplying the receiving countries with potential workers.
A 1998 British parliamentary inquiry noted that "a further motive was racist: the importation of 'good white stock' was seen as a desirable policy objective in the developing British Colonies".
Mr Balls said that while an apology would not "take away the suffering" it was important to the victims to admit it was wrong and to make sure lessons are learnt.
He said the government was talking to the victims' organisation to work out how to frame the apology.
"These were children who were shipped out of the country, often without their parents even knowing, went on to be labourers thousands and thousands of miles away, suffered physical and sometimes sexual abuse as well and it was something that was sanctioned by government and that is no way to treat children," he said,
"I think there have been discussions going on for some months about how to do this but to be honest it’s a matter of shame for our country and countries around the world that this terrible policy happened for so many years and decades and was actually government policy."
The issue of the UK child migrants was investigated in 1998 by the Commons health select committee, a process which led to the Department of Health drawing up guidance for families to trace those sent away.
Kevin Barron, the chairman, said Mr Brown wrote to him over the weekend to confirm he would issue an apology in the new year.
The Prime Minister told him "the time is now right" for the UK government to apologise for the "misguided policies" of previous governments.
However some survivors felt the apology was too little too late.
Harold Haig, the secretary of the International Child Migrants Association, said he was appalled that the Australian apology has come before any British apology.
"Gordon Brown should hang his head in shame," he said.
"He is allowing the country that we were deported to to apologise before the country where we were born. It is an absolute disgrace. He should hang his head in shame."