The country's largest supermarket chain said its subsidiary - Tesco Stores - had reached a Deferred Prosecution Agreement (DPA) over historic accounting practices with the Serious Fraud Office (SFO).
The deal emerged just days after Sky News reported an announcement was imminent, but it remains subject to judicial scrutiny on 10 April before it could take effect.
The SFO stressed that the DPA does not address liability of any sort.
Tesco was to pay, it said, a fine of £129m to avoid prosecution in relation to the £326m overstatement of profits in August 2014.
At the same time, the City watchdog said it had forced Tesco to compensate investors who had bought shares and bonds on - or after - 29 August and had held the securities when the profit figure was later corrected on 22 September.
The compensation bill was estimated by the Financial Conduct Authority at £85m.
Tesco said it would book a total charge of £235m - a figure that took not only the fine and compensation into account but also other sums including the SFO's full costs.
Its shares closed 0.7% higher as investors digested the news - and an entirely different development over major shareholder opposition to the chain's planned £3.7bn takeover of wholesaler, Booker.
Commenting on the proposed SFO settlement, Tesco's chief executive Dave Lewis, said: "Over the last two-and-a-half years, we have fully co-operated with this investigation into historic accounting practices, while at the same time fundamentally transforming our business.
"We sincerely regret the issues which occurred in 2014 and we are committed to doing everything we can to continue to restore trust in our business and brand."
The financial reporting scandal came to light shortly after Mr Lewis joined the company - dominating his time as the chain scrapped to recover sales lost to rivals in the supermarket price war.
Three former Tesco executives were charged last autumn with offences including false accounting and fraud by abuse of position, and are due to stand trial next year.
Chris Bush, the company's former UK boss; Carl Rogberg, the ex-UK finance director; and John Scouler, former UK commercial director have all indicated they will plead not guilty.