The all-rounder's future had become uncertain due to disagreements with the Australian coach, Mickey Arthur.
Watson said: "Making the decision to step down wasn't easy but it's something I've been thinking about since the Test series against India ended.
"I think it's the right time for a change for both the team and me. I'll be honest and admit I wrestled with the decision for some time, however once I made up my mind, I informed Cricket Australia so the selectors could consider their options for the Ashes given the squads will be announced soon."
Reports in Australia have suggested that the decision would have been made by Cricket Australia had it not been for Watson's announcement.