The transaction, which requires regulatory approval, is expected to complete in the second half of the year.
Allianz has also agreed to buy the 30 per cent stake held by LV= in their joint general insurance venture for up to £365m.
The sale marks LV=’s withdrawal from the partnership with Allianz owning 100% of LV=GI for a total consideration of up to £1.078bn.
L&G said the business being sold was primarily retail household insurance customers. In 2018 gross written premiums were £410m and operating profit was nil.
The insurer said it was “confident that selling the GI business to one of the world’s largest property and casualty insurers will mean that customers can trust they are in safe hands”.
The deal has a base price of £242m payable at completion and potential further payments over a three-year period from ongoing commercial arrangements.
Proceeds will be reinvested in its core businesses.
Nigel Wilson, CEO of Legal & General said: “Selling the general insurance business is the right decision for our customers and shareholders. And I would like to take this opportunity to thank our GI colleagues for their contribution to Legal & General.
“We continue to focus on delivering against our strategy, allocating shareholders’ capital rigorously.
“Our GI customers will benefit from the strength and capability of Allianz in the household insurance sector,” he added.
Allianz UK CEO Jon Dye said: “This is a good outcome for all the parties involved and acquiring a high quality business with two million customers to combine with the LV= GI business is a strong result.”
The transaction with LV= will close on 31 December and follows Allianz acquiring an initial 49 percent stake in LV=GI for £500m in 2017.
An agreement for Allianz to purchase a further 20.9 percent stake for £213m at the end of 2019 was already agreed, and the further 30 per cent sale announced today will be added to that.
LV= will retain the right to dividends from the 2019 LV=GI financial results and will continue to licence its brand to the general insurance business.
LV= group chief executive Richard Rowney said: “We have successfully grown the value of our general insurance business to in excess of £1bn and this deal enables us to realise that value for the long-term benefit of our members as well as strengthening our overall capital position.”
He added: “We have recently announced plans to convert to a company limited by guarantee which will provide greater flexibility and freedom to compete over the medium to long term as we continue to build on our heritage and strong brand to create a better mutual for the future, where being a member has more meaningful benefits.”