Crytek has confirmed that CryEngine now has "full native Linux support." A demo of the engine running on the open source OS will be presented at Game Developers Conference next week.
CryEngine has been used to power visually impressive games like Ryse: Son of Rome and Crytek's own Crysis series. Today's announcement marks a big step for the OS, which has big support behind it thanks to Valve and their efforts with SteamOS, a variant of Linux.
One of the next big games to use the engine is Turtle Rock's Evolve. While not yet confirmed, it's likely that CryEngine's move to Linux will help facilitate having more big games arrive on the platform.