The chain, which was set up in 1978 and is now among the UK's biggest retailers with 373 stores and 16,000 staff, saw its shares rise in conditional dealings from an opening price of 270p to as high as 289p at one stage.
Manchester-based brothers Simon, Bobby and Robin Arora, who bought the chain in 2004, will get another payday from the float, having already received an estimated £900 million when they sold a controlling stake to private equity firm Clayton, Dubilier & Rice (CD&R) in December 2012.
Selling shareholders, including the Aroras and funds managed by CD&R, will pocket £1 billion in the flotation, while the company itself will receive £75 million. Around 40% of the shares are being made available in the float.
Chief executive Simon Arora said: "We believe that becoming a public company gives us the right long-term ownership model, allowing us to build on our strong track record as we move to the next stage of development."
Seen as a modern-day Woolworths, B&M has boosted its fortunes in recent years by branching out into clothes, pet food and toiletries, as well as through the opening of more stores away from its northern heartland. It has said it believes there is potential for up to 600 outlets.
Liverpool-based B&M's chairman is the former Tesco chief executive Sir Terry Leahy.