The billionaire businessman, who owns a raft of high street clothes shops including Topshop, told a Sunday newspaper that it would be about 10% cheaper on branded goods than the big four supermarkets.
It comes as the major grocers - Tesco, Asda, Sainsbury's and Morrisons - face a squeeze as discounters Aldi and Lidl gnaw away at their market share.
Morrisons recently announced that it would spend £1 billion to slash prices over three years - after annual results showed it had tumbled into losses - while Asda is also spending heavily to make reductions.
Sir Philip's BHS is to see its first two shops to offer food, in Staines and Warrington, within days - with plans for about 140 such outlets.
He said: "There's no point in opening up and getting torn apart because we haven't got competitive prices.
"We know what we're going into - the most competitive food landscape for some time.
"On the basis that everyone is going into the high street and convenience, maybe it's an opportunity.
"If you don't buy a ticket, you can't win the lottery."
The openings will reportedly see sections of stores set aside for branded products such as bread and cakes, frozen items and soft drinks.
The idea that Sir Philip was considering launching food stores within BHS shops was floated publicly last year.
The business used to sell food before he bought it in 2000.