Yesterday the feature list for the Safari 10.1 release was posted, this release is now in Beta and includes Grid. The work to implement grid in Safari has been completed by the team at Igalia, who also implemented it in Blink.
This news means that in a few weeks time CSS Grid Layout will land in Chrome, Safari and Firefox.
I am keeping the browsers page on this site up to date as we approach shipping.
I have also written a few posts over on my blog about Grid Layout and browser support: