The former SABMiller brands include the Czech Pilsner Urquell, Poland's Tyskie and Hungary's Dreier.
AB InBev is working to close the deal as part of its efforts to pass competition regulations after its £79bn takeover of SABMiller.
Asahi, on the other hand, continues to branch out of its home market where prospects are bleak. Analysts at Cavendish Corporate Finance said Asahi has set aside nearly $4bn (£3bn) for overseas acquisitions as it looks outside Japan's shrinking domestic market.
Asahi said in a statement the acquisition, which is the largest purchase of a foreign beer operation by a Japanese brewer, will lift its overseas sales as a proportion of total sales to nearly a quarter, from 16 percent in October.
The combined deals show Asahi is a leading player in the international beverage market, said Jonathan Buxton, partner and head of consumer at Cavendish.
Consolidation in the brewing business is accelerating, and we can expect cash rich Japanese buyers to continue their ambition growth strategies by pursuing overseas acquisitions.
Asahi shares fell 6.4 per cent after the report before rising to 4.6 per cent at the market close.
The deal is expected to close in the first half of 2017.