October 27 to be exact. That's less than two weeks away.
You can sign up for the Beta here.
But this is no ordinary Beta. It's going to oscillate between a 'closed beta', made up of a small amount of testers who'll have regular access to the Beta, and Beta Test Weekends, where Blizzard will "open up the floodgates" in an attempt to test the Overwatch servers on a grander scale.
The first Beta Weekend is scheduled after Blizzcon, so my guess is either November 7 or the weekend after that, starting November 14.
Blizzard explained their reasoning:
"We're aiming to accomplish two primary goals with our public beta test: First, get tons of top-notch feedback on the gameplay—including balance, feel, and fun—to help us make Overwatch the best team-based shooter on the planet. Second, we want to hammer the heck out of our tech, including stress-testing our server infrastructure and making sure the game runs great on the widest variety of systems possible."
The Beta is Windows only and it goes without saying that you'll need to have Battle.net installed to play.
You can find out more about the Beta here.