The 2TB version will be rolling out to "select regions" on that date, Major Nelson announced on the Xbox Wire. The other models - 1TB and 500GB - won't arrive until later on, with no specific date given.
If you haven't pre-ordered an Xbox One S Microsoft says you can still do so, either through the Microsoft Store or from one of many retailers, and get it on August 2.
The new console is 40% slimmer than the existing Xbox One and introduces support for 4K video. It also comes with a built-in power brick (hooray!), an IR blaster, and a redesigned controller.
The 2TB console costs US$399 (AU$549/£349), while the 1TB and 500GB versions cost US$349/£299 and US$299/£249 respectively (Australian 1TB and 500GB versions have not been announced).