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The agreement was reached with policyholder advocate Clare Spottiswoode and was a flexible offer that reflected the value of the inherited estate pot, Mark Hodges, chief executive of UK life business of Aviva, said.

The final payments will be made to customers in its CGNU Life and Commercial Union Life Assurance Company with profits funds and will be based on the average value of the inherited estate for the three-month period from June to August.

This calculation will be made before a High Court hearing to approve the deal, planned for September this year.

The remaining 10 per cent of policyholders are expected to receive greater payments.

Mr Hodges said the majority of the cash payouts would be tax-free and payments were expected to start by November.

He said: "This is a good deal for our customers and shareholders. We have worked hard with Ms Spottiswoode and her team to come up with a flexible offer which accommodates the exceptional market conditions but still represents good value for the vast majority of our eligible customers."

Ms Spottiswoode, who represented the interests of policyholders, said: "This is good news for policyholders after the turmoil in the financial markets that affected the plan announced last year. This offer is also good for the great majority of policyholders under the FSA's current rules.

"The Aviva proposal shows that together we have found an imaginative way of keeping the reattribution in place which includes the opportunity for policyholders to benefit from any increase in the estates.

"Policyholders who decide not to accept the offer and keep their rights to future special distributions are also protected."

Aviva will now write to the 1m policyholders in two of its with profits funds with details of the revised reattribution offer.

The restructuring replaces an original offer made by Aviva earlier this year, which it then pulled back from due to the fall in value of its with profits fund on the stock markets and in the property sector, which had drawn on its reserves of surplus capital.

The reattribution process dates back to 2005 when Ms Spottiswoode was hired as an independent policy advocate to find a fair deal between policyholders and shareholders.

Amanda Davidson, director of London-based IFA Baigrie Davies, said: "I think the offer is reasonable given today's investment climate and each individual policyholder will make up their minds of what they want to do when they see the offer on the table."