Ministers said the move will ensure that those affected are not left out of pocket as they and the Post Office work toward full settlements for the "immense hardship" they have faced.
Earlier this week the Court of Appeal cleared 12 more former subpostmasters who were wrongly convicted of offences, bringing the total number of judgements overturned to 57, but hundreds more are hoping for similar decisions.
Between 1999 and 2015, they were sacked or prosecuted after money appeared to vanish from accounts at their branches.
The problems were caused by the Horizon computer system in Post Office branches which turned out to be flawed.
Some subpostmasters were imprisoned after being convicted of stealing money.
The Post Office is contacting postmasters and will aim to make an offer for an interim payment within 28 days of receiving an application from those whose overturned convictions relied on Horizon evidence.
Postal Affairs minister Paul Scully said: "The suffering and distress these postmasters and their families have gone through cannot be overstated.
"While nothing will make up for the years of pain they faced after this appalling injustice, I hope this initial step provides a measure of comfort.
"The Post Office has started to turn a corner in terms of dealing with its past mistakes - and this Government will support them in doing so wherever possible."
Post Office chief executive, Nick Read, said: "Ensuring compensation is made as quickly as possible is a priority for Post Office. I welcome the Government's support to enable these interim payments that begin to provide some redress to people who were badly failed.
"Whilst we cannot change the past, this is an important step towards meaningful compensation for victims and we will offer payments as soon as possible."
Chi Onwurah, shadow business minister, said: "This is long overdue, and a victory for the sub-postmasters who have been fighting tooth and nail to secure justice for those affected in this horrendous scandal.
"Today's news is bittersweet. For those sub-postmasters who lost their jobs, homes, and reputations. For those who have still not had their convictions overturned and so will not be in scope, and for those who lost their lives, for whom this news comes too late.
"We will look closely at the compensation Government is proposing, because it remains baffling that the issue of compensation has been excluded from the Horizon Scandal Inquiry's terms of reference. Labour will continue to press ministers to expand the inquiry's remit.
"The Government must uncover the truth about how this terrible miscarriage of justice can ever have happened and hold those involved accountable."