Update: Blizzard has corrected its tweets; the patch is June, not July.
A series of tweets from Blizzard just before the holiday weekend have confirmed that Overwatch’s competitive mode isn’t coming until later this summer — “mid-to-late July.”
https://twitter.com/PlayOverwatch/status/736331124645863424
Kotaku pointed out that competitive play was originally planned for closed beta and was disabled to be re-designed and implemented “sometime after Overwatch launches.” Lead Game Designer Jeff Kaplan told players a week ago that the mode would be back in time for the game’s first major patch. One might therefore conclude the first major patch will also be dropping in July.
Sorry about this! Competitive Play will be coming later in *JUNE*, not July. Apologies again for the error. 😖
— Overwatch (@PlayOverwatch) June 1, 2016
Thanks, Crow!