Video report by ITV News Business Editor Joel Hills
Retail mogul Sir Philip Green has agreed to pay £363 million to rescue the BHS pension scheme.
He said that the amount, which is less than the £571 million deficit the company was left with when it went bankrupt last year, represents a "significantly better" outcome than the schemes in the Pension Protection Fund (PPF).
The collapse of the high-street giant last April left thousands without jobs, and the deficit in the pension scheme affected around 22,000 holders.
The fallout sparked a lengthy parliamentary inquiry and left its high-profile former owners potentially facing a criminal investigation.
MPs also called for the billionaire to have his knighthood taken away.
But Sir Philip said that the settlement brings "this matter to a conclusion" and apologised to affected pensioners.
Sir Philip said: "I have today made a voluntary contribution of up to £363 million to enable the trustees of the BHS pension schemes to achieve a significantly better outcome than the schemes entering the Pension Protection Fund, which was the goal from the outset.
"The settlement follows lengthy, complex discussions with the Pensions Regulator and the PPF, both of which are satisfied with the solution that has been offered.
"To achieve a significantly better outcome than entering the PPF, the contribution required to achieve this long-term solution was arrived at by the actuaries for both The Regulator and the Trustees."
He added: "Once again I would like to apologise to the BHS pensioners for this last year of uncertainty, which was clearly never the intention when the business was sold in March 2015.
"I am also happy to confirm that any of the pensioners that have faced cuts over the last year will now be brought back to their original BHS starting level pension and will all be made whole.
"I hope that this solution puts their minds at rest and closes this sorry chapter for them."
TPR Chief Executive Lesley Titcomb said: "The agreement we have reached with Sir Philip Green represents a strong outcome for the members of the BHS pension schemes. It takes account of the interests of both pensioners and the PPF, and brings a welcome level of certainty to present and future pensioners.
"Throughout our discussions with Sir Philip and his team, we have always been clear that we were determined to achieve the right outcome for members of the schemes both in terms of the amount and the structure of the settlement."
Frank Field, the Labour MP who co-chaired a parliamentary inquiry into BHS' demise last year, said: "I welcome this out-of-court settlement and it is an important milestone in bringing justice to BHS pensioners and its workers."
He added: "I think there are a lot of other issues which are not solved by this which we will obviously be looking at and the courts and everybody else will be.
"It's not justice, but it is a milestone."
A Downing Street spokesman said: "We welcome the fact that the pensions regulator has agreed this settlement with Sir Philip Green.
"It is a positive outcome which will bring peace of mind to the 19,000 BHS pensioners who have endured a period of uncertainty since the company collapsed."