AB InBev had previously made offers of £38, £40, £42.15 and £43.50, all of which had been rejected.
The agreed offer represents a premium of 50% on SABMillerís share price of £29.33 a month ago, when AB InBev first expressed an interest in the acquisition.
AB InBev has made a separate offer to SABMillerís two largest shareholders, US tobacco company Altria and the BevCo investment vehicle owned by the Columbian Santo Domingo brewing dynasty. Together, they own 41% of SABMillerís shares.
Altria and BevCo have been offered a cash-and-share alternative involving AB InBev shares valued at £35.25 and cash at £3.78 a share.
The revised deal also allows for SABMiller shareholders to receive dividend payments through to March 31, 2016.
The offer values SABMiller at £68bn. AB InBev will pay for the deal in part through the issue of new debt.
The takeover will be the third largest in history and the largest ever of a UK-listed company.
SABMillerís stock rose 9.1% to £39.46 when trading reopened this morning.
The offer has yet to be formalised, but agreement had to be reached before the Takeover Panelís deadline of 5pm tomorrow, October 14. AB InBev now has until October 28 to make a firm offer.
The proposed merger is likely to face scrutiny from competition authorities around the world, most notably in the US where the combined market share tops 70%.
It is likely that a series of divestments will follow as the merged company seeks regulatory approval.
If AB InBev fails to get approval for the acquisition, or if its own shareholders reject the deal, it will have to pay SABMiller a £1.9billion break fee.