SABMiller said it had agreed "in principle" a £44-a-share offer, after four previous attempts from AB InBev.
AB InBev's brands include Budweiser, Stella Artois and Corona, while SABMiller produces Peroni and Grolsch.
If the deal, worth about £70bn, goes ahead, the newly-created firm will make about 30% of the world's beer.
SABMiller has a workforce of close to 70,000 people in more than 80 countries, and global annual sales of more than $26bn. AB InBev has a workforce of 155,000 and global revenues of more than $47bn.
Global market share of five biggest beer companies
Anheuser-Busch InBev - 20.8%
SABMiller - 9.7%
Heineken - 9.1%
Carlsberg - 6.1%
China Resources Enterprise - 6%
Source: Euromonitor, based on 2014 figures
AB InBev had made four previous bid approaches for SABMiller - at £38, £40, £42.15, and £43.50 per share - but they had been rejected by SABMiller, which argued they undervalued the company.
In a statement, the boards of the two firms said they had now "reached agreement in principle on the key terms of a possible recommended offer".
The two companies have not yet formally finalised the terms of an offer, but the latest development means they have extended the City deadline for a firm offer until 28 October.
The latest proposal comes a day before the original deadline, by which AB InBev had to make a formal bid for SABMiller or walk away for six months.
The offer represents a premium of about 50% over and above SABMiller's share price in mid-September, before the bid battle started.
In morning trade in London,
SABMiller's share price
rose 9% to £39.48, while shares in AB InBev were 2.85% higher at €101.15 in trading in Brussels.