Shadow chancellor John McDonnell said the payments were to settle a "historical debt of honour" to the women born in the 1950s, have dubbed their campaign WASPI (Women Against State Pension Inequality).
It follows a lengthy campaign by the so-called "Waspi women" who said they were given insufficient time to prepare for the changes brought in by the former coalition government.
Boris Johnson was challenged by one of the women in the studio audience for Friday night's BBC Question Time special.
The Prime Minister said that while he sympathised deeply, he could not promise to "magic up that money" for them.
Mr McDonnell said: "We've prepared a scheme to compensate these women for a historical wrong.
"It's one that they were not been able to prepare for and for which they've had to suffer serious financial consequences for as a result.
"These changes were imposed upon them by a Tory-led government. So we have a historical debt of honour to them and when we go into government we are going to fulfil that debt."