Private equity firms TowerBrook Capital and Warburg Pincus have been holding discussions with bosses for nearly a month and said they would offer shareholders 35p a share.
AA listed on the London Stock Exchange in 2014 at a price of 250p a share but this soon plunged and is seen as one of the poorer attempts by a company to cash in on a stock market listing.
The deal will see the new owners invest £380m into the business to pay off high debts and loan repayments due next year, racked up during over-expansion.
Bosses at AA said they will recommend the offer, having announced in May that they had been reviewing ways to support the business's high debts.
The AA said: "The board believes that the company needs a more sustainable capital structure and requires a significant amount of additional new equity in order to reduce the group's indebtedness and to fund future growth."
Suitors had been circling the company since August – despite the Covid-19 crisis seeing fewer journeys being made and limiting AA's opportunity to offer its services as a result.
Previous talks with Centerbridge Partners Europe and Platinum Equity Advisors had broken down but TowerBrook and Warburg Pincus stepped in last month.
However, some shareholders were concerned that the new owners may walk away from the deal following weeks of speculation and no sign of an offer and a deadline extended three times.
Drew Dickson, of Albert Bridge Capital, which owns a 20 per cent stake in the AA, reportedly said: "The private equity guys are obviously being smart by wanting this to draw out.
"We are happy for the AA to make this the final deadline. We would like to see them tell the other side: 'Listen, give us a price, or stop wasting all our time'."
AA was one of the most high-profile listings in 2014, with armchair investors keen to buy into a company that was founded in 1905 and remains a household name.
But the previous owners pumped the firm full of too much debt and a swift listing price of 250p jumped at points to 450p a share, before plummeting and never fully recovering.
During 2017 there was also a boardroom brawl that saw executive chairman Bob Mackenzie sacked following a fight in a hotel bar where a meeting had been taking place.
The firm was founded by four driving enthusiasts in London to warn fellow drivers about speed traps, initially calling itself the Motorists' Mutual Association but taking on its current name a month later. It now says it has grown to become the UK's largest motoring organisation with more than 15 million members – and the largest fleet of roadside patrol vans in the UK.
Additionally it has branched out into finance, insurance, leisure and lifestyle services.