Both sides said in a statement announcing the deal on Monday that the partnership will focus solely on BAT's "potentially reduced risk products" with an emphasis on technology and innovation.
"McLaren Applied Technologies will work with BAT on areas including battery technology and advanced materials. The two companies will share best practice, innovation know-how and mutual experience," it added.
Tobacco advertising was widespread in Formula One until a ban in 2006 led most teams to kick the habit and seek sponsors elsewhere.
Ferrari's partnership with Philip Morris International, whose Mission Winnow initiative focuses on smoke-free 'heat not burn' products and is the team's title sponsor, has been going for more than 40 years, however.
BAT, the world's second-biggest international tobacco company by revenue, bought Tyrrell in 1997 and competed as British American Racing (BAR) from 1999 to the end of 2005 when Honda took over.
Honda then quit at the end of 2008, handing over to principal Ross Brawn, who led them to victory in both championships under his own name in 2009.
In 2010 they became Mercedes, which has won both titles for the past five years.