Thompson is a marketer with 20 years’ experience working with brands including Guinness, PlayStation, Toyota, O2 and Pepsi, agency and client-side.
He will join Paddy Power in June, from his most recent role as chief marketing officer of customer engagement technology business Thunderhead, where news of his arrival only broke in January this year.
Before his role at Thunderhead, Thompson was the global director of business innovation at Telefonica, a company he spent seven years at, in posts including director of marketing innovation for Telefonica and O2 head of UK brand strategy.
He has also worked agency-side, including at TBWA/London, and founded Giffgaff in 2009, becoming the budget network's early-stage chief marketing officer.
At Paddy Power, he will fill the vacancy left by Woolfenden, who was promoted at the tail end of last year to the post of managing director of retail for the UK and Ireland, as part of a wider management shake-up.
Thompson will be responsible for "the strategic direction of the Paddy Power brand, entertaining our customers and wowing them with our differentiated product", the betting company said in a statement.
Thompson said: "I have always been a huge fan of the Paddy Power brand. The brand is overflowing with creativity, entertainment, disruption, innovation and mischief.
"To be asked to be CMO of such a unique proposition is a real honour. This really is my perfect job, and I cannot wait to get cracking."
Andy McCue, Paddy Power’s chief executive, said: "I am thrilled to welcome Gav to Paddy Power. He is a world-class marketing talent, and his passion for customers, brand experiences and innovation matches perfectly with Paddy Power’s."