The deal would create the world’s largest listed tobacco company.
BAT currently owns 42.2% of Reynolds and the proposal involves the acquisition of the remaining 57.8% of the company.
BAT chief executive Nicandro Durante said: “We have been a shareholder in Reynolds since its creation in 2004 and have benefited from its growth in the US market.
“The proposed merger of our two great companies is the logical progression in our relationship and offers all shareholders a stake in a stronger, truly global tobacco and next generation products company.
“BAT is proud of its track record of consistent delivery for shareholders and this transaction would further strengthen that delivery in the future.”
The offer would value the 57.8% stake at 56.50 US dollars (£46) per share, representing a 20% premium against the closing price of Reynolds shares on October 20.
The merger has yet to be approved by Reynolds’ board of directors. If given the green light, the deal would also be put forward to both BAT and Reynolds shareholders.
The Reynolds acquisition would add to BAT’s portfolio of 200 tobacco brands. The company currently employs more than 50,000 people globally and sells its products across 200 markets,
The group reported £5 billion in adjusted operating profit in 2015.
BAT said the deal with Reynolds would create a tobacco company with the largest global profit pool, excluding China.
The firm would also have a leading position in the US, and a significant presence in high- growth markets including South America, the Middle East and Africa.