Stroll runs the Racing Point F1 team, which will change its name to Aston Martin F1 for the 2021 season.
The Canadian tycoon will become executive chairman once the deal completes.
As part of the transaction, the luxury car group will raise £500mln through share issues with Stroll also providing a £55.5mln short-term loan.
A placing now will raise £182mln at £4 per share and give Stroll a 16.7% stake.
This will be followed by a rights issue for a further £318mln after the results for 2019 are published.
The Stroll consortium will invest £235mln in total.
Existing shareholders Prestige/Strategic European Investment Group (SEIG) and Adeem/Primewagon will take part in the rights issue but their holding will reduce to 50.5% from 61%.
Penny Hughes, Aston Martin Lagonda Chair, said: "The difficult trading performance in 2019 resulted in severe pressure on liquidity which has left the company with no alternative but to seek substantial additional equity financing.
"Without this, the balance sheet is not robust enough to support the operations of the group. Notwithstanding recent weak trading, the strength of the Aston Martin brand and our expanding portfolio of cars has allowed us to attract a strong new partner in Mr Stroll to support the turnaround of the business."
Aston Martin has had a torrid time since it listed in London in October 2018.
Shares in the carmaker started to drop almost immediately from their £19 float price as commentators suggested it had been seriously overpriced.
Synonymous with James Bond ever since Sean Connery drove a DB5 in Goldfinger, Aston Martin laid bare its problems in January when the 100-year old carmaker warned 2019 earnings would be around half the previous year.
Recovery hopes have been pinned on its first SUV, the DBX, where orders have been healthy but January’s warning raised concerns about whether the company had the cash to market it effectively.
Aston Martin’s debt is heading towards £900mln and its rivals are ploughing money into electric vehicles.
The Stroll- led team contains a number of high profile business leaders and reportedly fended off a rival plan from Chinese carmaker Geely.
JCB boss Lord Bamford, John Idol from clothing outfit Capri, fashion investor Silas Chou and cellular millionaire John McCaw are also part of the seven-strong consortium.
Shares rose 18% to 475p.
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