The food delivery company said on Sunday it had raised a further $180 million from existing investors, including minority shareholder Amazon, in a move that values the business at more than $7 billion.
Deliveroo is set to hold an IPO in the coming months, in what would be the biggest new share issue in London for three years.
Wolfson's appointment comes after Deliveroo named Claudia Arney as the company's first chair in November.
Deliveroo founder and CEO Will Shu said Wolfson would bring "great knowledge and insight" to the board.
Wolfson has been Next's CEO since 2001.
He is also a peer of Britain's ruling Conservative Party, sitting in the upper house of parliament.
(Reporting by James Davey and Paul Sandle; editing by Sarah Young and Pravin Char)