Firefox have indicated they intend to ship Grid in March. The release date for Firefox 52 is listed as the 7th March 2017.
Igalia have posted the Intent to ship for Grid into Chrome 57, estimated release date March 14th 2017. Opera is slated for around the same time. Perhaps this is the same for Chrome for Android, but I couldn't find any references.
Apparently IE 11/10 uses the old spec for CSS Grid however, there is no intension to update these browsers with the new spec. Edge is in the works but I can't find any reference to when it will ship.
There doesn't seem to be anything official from Apple, even though the Technical Preview browser has it enabled, there is no guarantee it will be in the next version of Safari....
