Rumbol, who has spent more than 10 years at the brewer, most recently as board-level marketing director, is joining Cadbury Trebor Bassett as marketing director, GB & Ireland.
He will replace Louise Cooke, who has been promoted to business development director for Africa, the Middle East and Turkey.
Inbev has yet to replace Rumbol, but is understood to be recruiting externally.
In his time at the brewer Rumbol has overseen some of the UK's biggest brands, including Stella Artois, the country's biggest alcohol brand, and the recent roll-out of global beer brand Brahma.
He has courted controversy in the past by ditching the "Heineken reaches the parts other beers can't reach" strapline in 1998 in favour of "How refreshing".
Rumbol worked on the Toblerone and Dime brands at Kraft Foods before moving into the drinks sector.
His departure comes amid a raft of redundancies at Inbev.
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