Update:
In a new post on the PlayStation Blog, Sony has confirmed that PlayStation Now is coming to Windows PC on August 24 in the UK, Belgium, and Netherlands. It will then release in the United States and Canada “shortly thereafter.”
For PS Now on PC, Sony says a minimum 5Mbps connection is required, and these are the recommended specs:

Windows 7 (SP1), 8.1 or 10
3.5 GHz Intel Core i3 or 3.8 GHz AMD A10 or faster
300 MB or more; 2 GB or more of RAM
Sound card; USB port

Sony also confirmed the DualShock 4 USD Wireless Adaptor, which releases in early September in North America for $24.99 and on September 15 in Europe:

This adaptor will let you connect a DualShock 4 to PC and Mac wirelessly, and will enable every feature of the controller you know and love: buttons, analog sticks, touch pad, light bar, motion sensors, vibration, and stereo headset jack ? as long as the gaming application supports these features. The adaptor is a great match for playing PS Now on a computer, but you can also use it for PS4 Remote Play on PC and Mac. If you haven?t yet downloaded Remote Play on your PC or Mac, grab the installer here. Of course, owning the USB Wireless Adaptor isn?t required, as you can connect a DualShock 4 using a USB cable.

A North American date for PS Now on PC will be confirmed soon, with Sony adding that we should “stay tuned for some exciting games that will be added to the library.”
[Source: PS Blog (1), (2)]
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