Watson has led BT's TV business since 2009 and is credited for being a key member of the executive team that launched its pay-TV challenger BT Sport.
Having previously worked for the consultancy Reel Enterprises, which advised the Premier League on its rights auctions, he helped BT secure the exclusive live rights for the Barclays Premier League, Aviva Premiership Rugby, the UEFA Champions League and UEFA Europa League.
He has overseen the growth of BT TV, a service enjoyed by more than 950,000 homes.
Watson said "I have had a fantastic time at BT, enjoying many years in an amazingly fast and dynamic marketplace. I'm sad to leave but now is the right time for me to take on a fresh challenge.
"I am proud of what we have achieved in BT TV. We have built a top-quality TV service from scratch and BT Sport is thriving thanks to the great live sport we've secured. I am sure the business will go from strength to strength and I wish everyone at BT well."
Gavin Patterson, chief executive of BT Group, said: "Marc has been at the heart of our TV strategy and I am sad to see him leave. He leaves BT TV in good health and we will continue to build on the strong foundations he has helped lay.
BT said in a statement that the search for a new managing director of BT TV & Sport is "well underway", with external and internal candidates being considered. Watson's replacement will report to John Petter, chief executive of BT Consumer.