The proposed deal includes Fuller's cider, soft drinks, wine wholesaling and distribution business, as well as its beer and brewing operations.
This means Fuller's historic Griffin brewery and its Cornish Orchards, Dark Star and Nectar Imports brands will also move to Asahi's ownership.
Asahi Europe Limited will receive the beer business's brands, which includes London Pride, as well as the benefits of a licence "on a perpetual, global, exclusive and royalty-free basis".
Asahi will be able to use various Fuller's trademarks to sell Fuller's-branded drinks.
However, ownership of the trademarks will remain with Fuller's.
Asahi, under the proposed deal, will act as Fuller's key supplier to the London-based operator's pubs and hotels.
Fuller's chief executive Simon Emeny said: "This deal secures the future of both parts of our business, including protecting the heritage of the Griffin Brewery in Chiswick, which was particularly important to the Fuller's board."
He continued: "We remain incredibly proud of the Fuller's beer business, its history and the high-quality premium beer and cider portfolio that we have developed.
'Integral part of our history'
"Brewing has formed an integral part of our history and brand identity, however the core of Fuller’s and the driver of our future growth is now our premium pubs and hotels business.
"I am delighted this transaction maintains Fuller’s long association with the beer business and that we will continue to enjoy a strong relationship with Asahi as a key supplier.
"We look forward to continuing our alliance and developing a mutually beneficial partnership that will see both businesses flourish in the future.
"Asahi, as a company recognised for brewing excellence, is an appropriate custodian of our rich brewing history and the Griffin Brewery, and will ensure the Fuller’s beer business brands will reach an even wider global audience."
Asahi Europe CEO Hector Gorosabel welcomed the move, claiming it would further consolidate the brewer's position in the premium beer market.
He said "Our global footprint will enable us to unlock the potential in these brands internationally to significantly enhance their scale and value.
"It is another step towards realising Asahi Europe’s vision of becoming a global brewing powerhouse built on our commitment to brewing excellence and quality."