The PM said this will be offered to determine the "nerves and issues".
A few people who went to the UK from the Commonwealth decades back have been debilitated with expelling or denied employments or social insurance.
In the interim, it has risen that the National Archives hold landing records for a huge number of those individuals.
These records could help a portion of the Windrush age who are attempting to demonstrate they are in the UK lawfully.
It was uncovered not long ago that a large number of landing cards of Windrush transients had been demolished in 2010.
On Thursday, Chief Secretary to the Treasury, Liz Truss, Time that the legislature would "take a gander" at remuneration demands from Windrush migrants.
Mrs May's first open say of compensation came at a news gathering finishing up the Commonwealth Heads of Government Meeting (Chogm) in London on Friday.
She stated: "On Tuesday, I met with Caribbean pioneers, where I gave a flat out responsibility that the UK government will do whatever it takes - including where proper installment of remuneration - to determine the tensions and issues which a portion of the Windrush age have endured.
"These individuals are British, they are a piece of us, they assembled Britain and we are all the more grounded for their commitments."
More subtle elements on the plans are relied upon to be distributed inside the following week.
Work MP David Lammy, who has initiated the crusade for the Windrush age, said more detail was required from the legislature.
He said that "pay and reparations" ought to be given "to any individual who had lost their activity, their benefits, access to social insurance, or been confined or ousted".
Grenada's Prime Minister Keith Mitchell has likewise called for "genuine" pay in light of the PM's discourse, saying it was "exceptionally critical" she had said remuneration.
He stated: "It's not simply, 'I'm sad.' People lost a considerable measure, individuals endured a great deal of torment, and they should be given a chance to redress this - some genuine remuneration.
"If not the individual, on the off chance that they've gone, at that point the families who have endured as well."
In Pictures: The Windrush age
An aggregate of 286 individuals have reached the Home Office since Monday, when the office set up a helpline to help the individuals who had worries about their relocation status.
Up until now, eight have been given lasting living arrangement status.
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