BRUSSELS -- Anheuser-Busch InBev (BUD) has announced an agreement in principle with SABMiller to take over the brewer at 44 pounds ($67.63) a share. That would result in a company that is the world's biggest beer giant.

The brewer of Budweiser and Stella Artois said Tuesday it had increased its offer overnight for the world's second-largest brewer and that both boards "reached agreement in principle on the key terms of a possible recommended offer."

AB InBev has been trying for nearly a month to get its hands on SABMiller but its previous offers have met with resistance. On Monday, it was hoping that its latest offer, which valued SABMiller at 43.50 pounds a share - 14 percent higher than its initial offer - would finally win the day, but it still upped its offer.

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The Reuters news agency puts the value of the takeover proposal at $104.48 billion.

AB InBev had a Wednesday deadline to make a formal offer under U.K. takeover rules.

The combined company would have 31 percent of the global beer market, dwarfing the next biggest player, Heineken, which has 9 percent of the market. A combined company would have total annual sales of $73.3 billion.

Market leader AB InBev already has six of the world's largest beer brands. In addition to Budweiser, brands it owns include Stella Artois and Beck's. SABMiller, which is based in London, is the maker of rival brand Miller Genuine Draft, along with other names like Peroni and Milwaukee's Best.

Crucially for AB InBev, a deal would enable it to venture out more into the African and Australian markets where its might has yet to be felt in the way it is in Europe, North Africa and Asia.

Tensions between the two companies have risen since the first offer was announced Sept. 16, with AB InBev accusing SABMiller's board of failing to engage meaningfully in negotiations. SABMiller has argued that the previous offers undervalue the company.

Any merger, however, is expected to draw scrutiny from regulators worried about how it might hurt competition and lead to higher prices for shoppers.

The beer industry has been consolidating for the past decade as it seeks to gain more clout with suppliers, distributors and retailers in a market that's seen overall slowing sales in the U.S.

In the U.S., overall beer sales rose just 0.5 percent last year, while mainstream brands like Budweiser were hurt by smaller beer brands with more cachet. Sales of craft beers climbed 17.6 percent in 2014 and accounted for 11 percent of the $101.5 billion market, according to the Brewers Association, a U.S. trade group of more than 1,900 brewers.

"The big macro brands that are really the cash drivers are now in decline," said Duane Stanford, editor of Beverage Digest, a trade publication. "People are more interested in diversifying and having more beverage choices. They want different flavors, more rich beers, more imported beers."