The original Overwatch servers will shut down on October 2

Blizzard said in an interview with Eurogamer that the original Overwatch servers will be offline on October 2 (Pacific time is given, so it could be October 3 depending on the country), and Overwatch 2 will launch on October 4 and will be the only version of Overwatch that works.

"So roughly a day before Overwatch 2 launches, we're going to be taking down the Overwatch 1 servers," commercial lead Jon Spector explained to me. "So that means, as a practical point, that October 2nd really is the last day to go in and play Overwatch 1. And then it's a 27-hour downtime that we're planning in order to get the Overwatch 2 server stood up and running.

Players will be given the opportunity to download Overwatch 2 just before it officially launches. You don't need to download the sequel - you just click the "Upgrade to Overwatch 2" button. Note that the pre-load will only be available to Overwatch 2 players. New players will have to wait until October 4. With the release of the game the company will release instructions on how to upgrade.

Source: Eurogamer