The shares floated at 240p, rising 3% or 7.25p to 247.25p amid strong institutional demand for the shares — giving Worldpay a market value of over £4.8 billion.
Worldpay traces its history back to 1989, when it was an electronic payments firm known as Streamline.
It was bought by RBS in 2002, which renamed it.
After the taxpayer bail-out of the bank, RBS had to sell it to comply with European state aid rules.