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The stock fizzed up 71p, or 1.8%, to 4047p in London while AB Inbev's shares rose €2.10 to €113.30 in Brussels.
AB Inbev, which makes Stella Artois, said the long-awaited deal would value Peroni brewer SABMiller at £44 per share.
The Belgian group said the deal would create a company with operations in virtually every major beer market and provide more choice for drinkers.
It would strengthen AB InBev's position in key emerging regions with strong growth prospects such as Asia, Central and South America, and Africa.
AB Inbev said in a statement: "In short, AB InBev believes more can be achieved together than apart."
But the pair are likely to have to sell off large parts of their operations to gain approval from competition regulators.
AB InBev has already agreed to the sale of SABMiller's 58% interest in US and Puerto Rico joint venture MillerCoors to partner Molson Coors for US$12bn.
The deal will give Molson Coors, which has a UK brewery in Burton-on-Trent in Staffordshire, full control of the company that makes Coors Light.
Market analyst Josh Mahony at spread-betting firm IG said: "The resulting mega brewer would be head and shoulders above any other firm in the sector, and this is questionable in terms of the impact it would have upon competition.
"However, given that SABMiller has focused its efforts into Latin America and Africa, this is arguably a deal which would benefit shareholders rather than simply management."
The formal proposal follows a string of offers from AB Inbev that SABMiller turned down on the grounds that they undervalued it.
AB Inbev chief executive Carlos Brito said: "We believe this combination will generate significant growth opportunities and create enhanced value to the benefit of all stakeholders."
SABMiller chief executive Alan Clark said: "The SABMiller story is a simply amazing achievement, and everyone who has been a part of it should feel immensely proud of the value they have helped create.
"I am sure the next chapter will bring new opportunities for exceptional success."
Stella Artois brewer AB Inbev also makes Budweiser, Corona and Leffe, while Britain-based SABMiller - which holds second position - owns Peroni, Grolsch and Pilsner Urquell beers.
ABI employs about 1,000 people at its UK breweries in Magor, Samlesbury and Mortlake, as well as its company headquarters in Luton. It has at least 200 beer brands.
SABMiller has around 69,000 staff in more than 80 countries, from Australia, Zambia and Colombia to the Czech Republic, South Africa and the US, also producing more than 200 beers.
Formerly known as South African Breweries, SAB acquired US rival Miller Brewing Company in 2002, resulting in the renaming of the group as SABMiller.
A merged group would be worth about £177bn and would add AB InBev's dominance of Latin America to SABMiller's strong presence in Africa, as well as their breweries in Asia.