The Premier League said Dinnage will commence her new role early next year at a date yet to be agreed with Discovery.
"I am excited at the prospect of taking on this fantastic role," Dinnage, who becomes the first woman to hold the post, said in a statement.
"The Premier League means so much to so many people. It represents the pinnacle of professional sport and the opportunity to lead such a dynamic and inspirational organisation is a great privilege.
"With the support of clubs and the team, I look forward to extending the success of the League for many years to come."
Executive chairman Scudamore, who has been at the helm of the organisation for nearly 20 years, will relinquish his duties at the end of 2018.
The Premier League has decided to split his role with Dinnage taking over as chief executive. The search for a non-executive chair will now commence. (Reporting by Hardik Vyas in Bengaluru Editing by Toby Davis)
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