Shares in the firm, which was previously owned by Royal Bank of Scotland, were initially offered at 240p each after its private equity owners Advent International and Bain Capital sold a stake of about 51 per cent in the business.
The share sale will raise up to £2.5bn, of which £948 million will go to the company, which intends to use the cash to expand into new markets and develop its payments systems.
Worldpay processes about 31 million mobile, online and in-store transactions every day. It employs about 4,500 staff, mostly in the UK and US, which are its two biggest markets.
Advent International and Bain Capital were reported to have rejected an offer of up to £6.6bn, including debt, earlier this year from French rival Ingenico Group.
Worldpay chief executive Philip Jansen called the flotation a “significant milestone” for the business.
He added: “We are proud to be a leader in global payments with a clear strategy for continued growth as a listed company.
“We have already invested over £1 billion in our technology, people and capabilities, helping us to become an advanced and sophisticated technology-led organisation with great potential.”
Advent International and Bain bought Worldpay from RBS in 2010 for about £2bn.
London Stock Exchange chief executive Xavier Rolet said: “The fact Worldpay has chosen to raise capital here confirms London’s position as the leading global financial centre able to attract the world’s most important new companies and highlights the exceptional investor appetite for dynamic companies.
“We look forward to welcoming more fast growing British and international businesses to our markets.”
Worldpay saw its underlying earnings lift by 8 per cent to £375m last year.