The companies had been locked in talks ahead of a Christmas Day deadline.
A deal between the two firms would create a significant force in the motor insurance sector, estimated to cover more than a fifth of the total UK market.
Aviva chief executive Amanda Blanc said the deal is “excellent news” for both companies’ customers.
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“Aviva and Direct Line share a deep commitment to excellence in looking after customers and this will remain a top priority following the acquisition,” she said.
“The financial strength and scale of the combined group means customers will benefit from competitive pricing, an enhanced claims experience and even better service.”
The takeover will see Aviva pay 129.7 pence in cash and 0.2867 of its own shares for each Direct Line share.
It will also pay up to 5p in dividend payments per share to Direct Line shareholders as part of the deal.
Aviva shareholders will own approximately 87.5% of the new company while Direct Line shareholders will own about 12.5%.
Shareholders will get the chance to vote on the deal in March, with the merger completing in mid-2025.
Danuta Gray, chairwoman of Direct Line, said the deal “reflects the attractiveness of Direct Line”.
She said Direct Line’s board had been “very pleased” with the work of chief executive Adam Winslow since he joined the struggling insurer in March with the goal of turning it around.
But she added that the offer allows shareholders to “realise the value of their investment in the near term”.
Direct Line has been subject to a number of takeover offers this year after Mr Winslow joined in March following the ousting of Penny James from the top job.
The company has already fended off a takeover attempt by Belgian company Ageas this year.
Direct Line, which also owns the Churchill and Green Flag brands, has since announced £100 million of cost cuts and axed 550 jobs.
Mr Winslow said Direct Line is an “excellent business, home to many well-loved insurance brands, and this year we have made fast progress on our turnaround strategy”.
“Bringing Direct Line and Aviva together offers the opportunity to create a strengthened and enlarged business, with both organisations sharing a deep passion for serving customers and for supporting their people.
“In a highly competitive UK general insurance marketplace, the combined entity will be very well placed to deliver for its customers.”