Gibson is Chairman of HomeServe and has previously held director roles at William Hill and Bwin.
In March, Feldman sold 900,000 GVC shares at a price of £6.66 ($8.71) each, retaining 287,408.
There was some shareholder backlash at the sales, with CEO Kenny Alexander also selling a number of shares at the time.
Later that month, reports surfaced of Feldman being replaced, although GVC told Gambling Insider the recruitment process had started well before the aforementioned share sales.
Feldman has been in his role since 2008, with new corporate governance guidelines for public companies insisting the length of a chairmanship must not exceed nine years.
He has been a GVC board member for 15 years and will step down on 27 February 2020.
Gibson said: "I am delighted to be joining GVC at such an exciting point in its growth trajectory.
"I have been involved in a number of companies in the gambling sector over many years and it is immediately clear to me GVC has industry-leading technology, products, brands, marketing capabilities and people."
GVC’s share price dipped on the morning of the news, from £8.95 to around £8.50, although it had hitherto sharply risen since a low of £5.45 in August.
