One million Norwich Union policyholders are being offered pay-outs of around £1,000 each to give up their rights to surplus cash in the group's with-profits funds.
The insurer's parent company Aviva is offering qualifying members of two of its with-profits funds a total of £1 billion in exchange for giving up their rights to any future redistribution of the money.
It said 700,000 people can expect to receive between £400 and £1,000 if they accept the offer, while a further 220,000 will get between £1,000 and £3,500.
Eligible policyholders will learn the level of their pay-out later this year, with the payment likely to be made next summer.
The offer follows 18 months of complex negotiations between Norwich Union and the independent policyholder advocate Clare Spottiswoode.
Aviva said it thought the offer, which is being endorsed by Ms Spottiswoode, was fair, and represented good value for 99% of policyholders.
But policyholders do not have to accept the cash.
They can instead decline the offer and retain their rights to any future redistribution of the surplus cash, which is known as the inherited estate and has built up in the fund over many years.
But Aviva said that any sizeable distributions are unlikely, especially in the next few years.
The pay-out will come from Aviva's shareholder funds, leaving the £2.1 billion inherited estate in the with-profits fund to ensure it remains financially strong.
In February Norwich Union announced £2.3 billion of its inherited estate would be returned to policyholders and shareholders as part of a special distribution.
Policyholders are in line for 90% of the cash and shareholders will get 10%, with the money paid out over three years.
The combination of today's offer and the special distribution means that the equivalent of around 70% of the value of the inherited estate will be released to policyholders.
Ms Spottiswoode said the deal was in the interests of the "great majority of policyholders" and was "good in all respects".
She added: "This has been a long and difficult process. I have challenged many aspects of the rules of the with-profits industry to try to ensure that policyholders receive the best deal possible."
Policyholders in the CGNU Life and CULAC funds who had policies on November 21 2006 and still have them when the pay-out takes place next summer will qualify for the deal, as will people whose policies have matured since November 2006.
Details of the offer came as Aviva announced a 12% rise in half-year operating profits to £1.72 billion.
The bottom-line result showed losses of £1.27 billion after the group accounted for a reduction in the value of its assets in the current climate.
It said sales in the faster-growing markets of North America and Asia Pacific offset "the more challenging markets" of Europe, including the UK.
Aviva said it expected the UK market for life and pensions to remain "subdued" in the second half of the year, but added that it had managed to increase its share of a declining market over the first half of the year.
In general insurance, profits rose 15% to £326 million after weather conditions returned to normal compared with the previous year's floods.
Chief executive Andrew Moss said: "In the face of economic headwinds, Aviva has made real progress in the last six months."
He announced the company planned to increase its annual cost savings target by £150 million to £500 million, but did not provide further details.
The company recently warned of up to 1,800 redundancies as part of a restructuring of its general insurance arm over the next two years.
It will consolidate the operational functions of its Norwich Union Insurance (NUI) business into seven centres at Norwich, Perth, Bishopbriggs, Stretford, Manchester, Leicester and Southend.
In Birmingham, around 270 out of 600 staff at two offices will affected, although they will be offered the chance of redeployment. The firm’s CU House premises in Corporation Street are to go, but it will be retaining Lombard House in Great Charles Street.