The company's flotation is the largest on the London market so far this year. Its shares were initially offered at 240p each, after its private equity owners sold a 51% stake in it.
Worldpay processes more than 30 million mobile, online and in-store transactions every day.
The company employs about 4,500 staff, mostly in the UK and the US.
Company chief executive Philip Jansen described Worldpay's listing as "a significant milestone".
He added that more than £1bn had been invested in the company, "helping [it] become an advanced technology-led organisation".
Worldpay was sold by the Royal Bank of Scotland in 2010 to its current owners, Advent International and Bain Capital. In terms of money raised, the flotation also means it is Europe's largest private equity-backed listing.
In a statement, the London Stock Exchange Group said Worldpay's decision to list in the UK "confirms London's position as [a] leading global financial centre" and "highlights [an] exceptional investor appetite".
Payments processing firm Worldpay has listed on the London Stock Exchange in a sale raising more than £2bn.