Overwatch game director Jeff Kaplan recently answered a question regarding how many people are working on Overwatch, and the response was a lengthy one detailing the team and the different roles being filled. In short, there are about 100 people working on the game.
Among 'Team 4' (the Overwatch team) there are audio, art, engineering, production and design teams. There are also others beyond the immediate teams, such as licensing, that deal with the game as well.
Kaplan said "there are even more groups here at Blizzard that are helping us all the time. We have the world's best Customer Support team known to existence (fact). A great HR team... I know I am leaving out some well-deserving-of-praise folks -- and I apologise. But you can see, we get a lot of support. But at it's core, it's about 100 gals and guys trying to make cool stuff that makes you guys happy."