The Home Office is to start making payments as part of the Windrush scandal compensation scheme.
In a written statement to Parliament, Sajid Javid said: "The Government deeply regrets what has happened to some members of the Windrush generation and when I became Home Secretary I made clear that responding to this was a priority.
"The compensation scheme has been open to receive claims since April 2019 and the Home Office is now in a position to start making payments.
"I am committed to providing members of the Windrush generation with assurance that they will be appropriately and promptly compensated where it is shown that they have been disadvantaged by historical Government policy."
In April Mr Javid said he launched the scheme to "right the wrongs" of the scandal.
Thousands of victims will share in an estimated £200 million compensation fund under the two-year initiative after facing difficulties demonstrating their immigration status.
Up to 15,000 eligible claims are expected to be lodged, according to the Home Office.
Mr Javid told MPs there would be no cap on the total amount awarded and the £200 million figure was a "baseline estimate".
The funds will not be split between victims. Each application will be assessed individually and a level of payout decided.
An official impact assessment said the final figure could range between £120 million and £310 million.
Staffing costs are expected to be between £4 million and £6 million a year.
Opening the scheme, Mr Javid described the treatment of some members of the Windrush generation as "a terrible mistake".
But last week the Home Office was accused of being "reckless" for failing to monitor the impact of its so-called hostile environment immigration policy, according to a leaked draft review into the scandal.
Channel 4 News and the Joint Council for the Welfare of Immigrants obtained extracts from the review, which reportedly said the Government department "failed to monitor, or effectively evaluate, the effectiveness and impact of compliant environment measures".
"This appears particularly reckless considering the significant warnings that the department was given about their potential consequences," it said.