BAT, which currently owns 42.2 per cent of Reynolds, will pay £49.27 ($59.64) per share for the remaining 57.8 per cent of the company in an improved offer after originally tabling a £38.8 billion ($47 billion) approach in October.
The deal will bring together a raft of global brands under one roof, including BAT products Rothmans, Kool and Kent, and Reynolds' brands such as Newport, Camel, Pall Mall, Doral, Misty and Capri slims.
The offer comprises £20.6 billion ($25 billion) worth of BAT shares and £20.1 billion ($24.4 billion) in cash, valuing Reynolds at more than £70.2 million ($85 billion).
The sweetened deal represents a 26 per cent premium against the closing price of Reynolds' shares on October 20.
BAT is expecting to make at least £330 million ($400 million) in cost savings after the two companies merge.
Chief executive Nicandro Durante said: "Our combination with Reynolds will benefit from utilising the best talent from both organisations.
"It will create a stronger, global tobacco and NGP (next generation products) business with direct access for our products across the most attractive markets in the world."
The boards of both BAT and Reynolds will recommend the takeover to shareholders and have agreed a so-called break fee of up to 1 billion US dollars (£825 million) if either party pulls out or if the deal is blocked by regulators.
If given the green light, it is expected to complete in the third quarter of the year.
The agreement comes after Reynolds reportedly rejected BAT's initial offer in November.
The companies' combined earnings will be significant. BAT reported £5 billion in operating profit in 2015, while Reynolds reported pre-tax profits of £5.3 billion ($6.4 billion).
The takeover is expected to help BAT gain a further foothold in the US, and give the new company a significant presence in high-growth markets including South America, the Middle East and Africa.
BAT is also planning to use the increased might to expand further in the vaping and e-cigarette market - where it is already the largest international company outside the US - adding Reynolds' popular Vuse vapour brand.
BAT has more than 200 brands sold in some 200 markets and employs over 50,000 staff worldwide.
It claims to sell its cigarette brands to one in eight of the world's one billion smokers.
Reynolds is the second biggest player in the US market, with three out of the four top- selling cigarette brands.
The US firm has a 34 per cent cigarette market share, with Newport the leading brand in menthol, Pall Mall the leading value brand and Natural American Spirit, the fastest growing premium brand.
It has factories in North Carolina and Tennessee.
BAT first invested in Reynolds through a deal which saw BAT's US subsidiary Brown & Williamson merge with RJ Reynolds in 2004, giving BAT its original 42 per cent stake in the US firm.
In 2014, BAT pumped £3.9 billion ($4.7 billion) into Reynolds in order to maintain its stake in the company following a mega-deal which sawReynolds acquire sector peer Lorillard for £22.6 billion ($27.4 billion).