Griffith’s brief will be to improve the line of communication between business groups at home and abroad ahead of what could be a No Deal Brexit.
The incoming Prime Minister has pledged to leave the European Union by October 31, even if that meant doing so without an agreement.
Griffith was seen as a key figure during the broadcaster’s takeover by Comcast earlier this year.
In a statement, Sky chief executive Jeremy Darroch said: “Over the course of his 20 years at Sky and since 2008 as a member of the board as CFO (chief financial officer) and then as chief operating officer, Andrew has played a fundamental role in many of our proudest collective achievements.
“These include transforming the business from around three million customers in the UK and Ireland to over 24 million customers across Europe today, our successful entry into new markets such as broadband and mobile and building a business organically to become one of the UK’s most valuable FTSE 100 companies.”
Griffith begins his appointment Wednesday.