Blizzard has joined Riot (League of Legends) and Perfect World (Dota 2) in making its loot box drop rates available to the public in China. The message, via Google translate, says that each Overwatch "supply" will contain four items, with at least one of them being "excellent [rare] or higher quality."
It gets a little more interesting further down the list. An "epic" quality item will be awarded, on average, once every 5.5 loot boxes, while "legendary" items will appear once in every 13.5 boxes. Blizzard didn't provide percentages, but fortunately the good folks at PvP Live did the math (I did too, just to double check), and that works out to an 18.2 percent chance to pick up an epic, and a 7.4 percent chance to score a legendary, per loot box. Obviously, you'll always take home at least one rare item.
The law forcing game publishers to reveal their loot box drop rates was announced late last year, and came into effect on May 1. The relevant bit compels game publishers to reveal "information about the name, property, content, quantity, and draw/forge probability of all virtual items and services that can be drawn/forged" by players. They're also required to publicly track the actual "random draw results," so people can see how real-world drop results compare to the stated odds.
As with LoL and Dota 2, it's not known whether these rates apply internationally, or if they're specific to China. I've reached out to Blizzard to ask, and on the off-chance someone there is feeling forthcoming about it, I'll let you know what they say.