The home secretary has said that the current estimated cost of the Windrush Compensation Scheme was about £200 million.
Sajid Javid added that there is no limit to the amount which could be paid to the victims of the Windrush generation as he confirmed the compensation scheme has "no cap".
He told the Commons: "There's no cap to this scheme, no-one knows what the eventual cost will be, it will be based on the needs and the claims that are actually made by the eligible people.
"But the baseline estimate of my department is approximately £200m."
In a statement to MPs, Mr Javid said the "unacceptable treatment" experienced by some members of the Windrush generation was a "terrible mistake and it should never have happened".
Announcing details of the Windrush Compensation Scheme he acknowledged it had "taken longer than I would have liked", but added it was "vital that we get this right".
The government says the scheme "will provide payments to eligible individuals who did not have the right documentation to prove their status in the UK and suffered adverse effects on their life as a result".
It added: "These could range from a loss of employment or access to housing, education or NHS healthcare to emotional distress or a deterioration in mental and physical health."
People who were wrongfully detained or removed from the UK could also be able to make a claim.
Mr Javid said: "It was a terrible mistake and it should never have happened. And that it did is a matter of profound regret to myself, to my department, to the government."
The scheme took account of more than 2,000 responses to the call for evidence and consultation, and was not only open to those of Caribbean origin but any Commonwealth citizens settled in the UK before 1973.
The government, he said, also proposed to accept claims from the "estates of individuals who would themselves have been eligible had they not passed away and from close family members of an eligible person".