The title has "a limited-time exclusivity" for consoles but could see a simultaneous PC release.
In an interview with Kotaku, Jonathon Blow of "Braid" fame, explained the reasoning behind the PS4 as the debut platform, "People have been speculating that I got a money hat for this agreement with Sony, or that we needed to do this in order to fund development of The Witness. Actually, no money was involved at all.
"The real situation is that, because we are a small developer, we only have the ability to launch on a small number of platforms at once. We liked the idea of being on a console, and originally we thought we might be on the PS3 or Xbox 360, but eventually we decided not to target either of those due to the relatively low system specs... We were going to be a de facto console exclusive for Sony no matter what. As I mentioned, there are people at Sony who are very interested in The Witness, so they somehow percolated up through the ranks the idea of showing the game in the launch show. "
"Of course, Sony wants that show to point out things that are going to be exclusive or special to their console. So to be in the show we signed a timed exclusivity for competing consoles. But this was just a formalization of something that was already de facto. We like the PS4 and we like the people at Sony we are working with, so it was an easy choice to make the agreement."
Blow stopped just short of ruling out a port for the Wii U or "the next Microsoft console," "Our deal with Sony is a limited-time exclusivity that applies only to competing console platforms." When asked, Blow explained that the exclusivity does not apply to the PC or iOS, and left the door open for not only a PC or iOS version, but for a simultaneous release with the PS4 version.