Aviva outlined the offer as it announced a rise in operating profits
A million policyholders in two of Norwich Union's with-profit funds are to be made offers of payouts that will average £1,000.
About 700,000 people could receive between £400 and £1,000, and another 220,000 could get a payout of between £1,000 and £3,500 if they accept.
The payouts, worth a total of £1bn, follow long negotiations.
Aviva, which runs the Norwich Union brand, also announced a 12% increase in half-year operating profits to £1.7bn.
The latest offer is only for investors in two of Norwich Union's oldest funds - CGNU Life and CULAC with-profits funds. These are mainly customers with endowment policies, pension policies and with-profits bonds.
The payout comes from shareholders' funds to buy out policyholders' rights to any future claim on the surplus of the two with-profits funds - known as the "inherited estate".
This deal is good in all respects. It also provides a fair return to shareholders
Claire Spottiswoode Policyholder advocate
This surplus has largely built up because companies have put aside more money than they need as a financial cushion in the funds.
The amount offered to individual policyholders will be outlined later in 2008, and if accepted will probably be handed over next summer.
Policyholder advocate Claire Spottiswoode, an independent expert appointed to represent policyholder interests, has long been in negotiations over the payouts.
"This 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," she said.
She described the deal as in the best interests of the great majority of policyholders.
"This deal is good in all respects. It also provides a fair return to shareholders," she said.
In February, Aviva said 1.1 million policyholders would see bonuses worth a total £2.1bn added to policies.
But it has been in dispute with Ms Spottiswoode over the remaining £3.2bn.
In total, about 70% of the inherited estate is being transferred to policyholders, either as bonuses or cash, following the two announcements.
The Financial Services Authority now needs to ensure that the deal contains sufficient safeguards to protect policyholders' interests
Peter Vicary-Smith, Which?
Mark Hodges, chief executive of Norwich Union Life, said: "This is a great offer. We believe that it represents good value for 99% of policyholders and almost all of the cash payments will be tax-free.
"Most importantly, we recognise that policyholders have a choice and everyone will be entirely free to make their own decision on whether or not to accept the offer."
Individual policyholders can choose to turn down the offer, and retain their right for future claims on the inherited estate.
But Aviva warned that any payouts were unlikely in the next few years.
The Financial Services Authority (FSA) said that its preliminary assessment considered Aviva's offer to be "fair".
In June, the Treasury Select Committee criticised the FSA for failing to protect policyholders in with-profits funds.
Aviva's chief executive says the payout is good for shareholders and the UK economy
The group of MPs said not enough was being done to stop insurance firms managing the funds in the interests of shareholders rather than policyholders.
Peter Vicary-Smith, chief executive of consumer association Which? said that Aviva policyholders could have received more from the latest deal if the FSA had regulated the area effectively.
"The FSA now needs to ensure that the deal contains sufficient safeguards to protect policyholders' interests," he said.
"Policyholders deserve a regulatory framework based on a clear set of principles which guarantees that all inherited estates are used in their best interests. The FSA needs to act now."
Aviva is the first major UK insurer to report earnings for the first half of the year.
It said it expected the UK market for life and pensions to remain "subdued" in the second half of the year.
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