Mozilla is working on making WebExtensions available in Firefox (dropping XPCOM, XUL and jetpack); API will be the same as Chrome extensions.

Opera already have them.

Mozilla has announced they will come gradually through Firefox 44 to 48, with a stable release in july.

Microsoft is also working on them in Edge.

The WebEXtension API is broken in about 60 components; Chrome having 100% support, Opera probably 100% too. The status page for Firefox can be found at http://arewewebextensionsyet.com/

No trace of a public spec by the w3c, unfortunately :/ I don't even know if w3c is involved; but it is really great they are finally making efforts into providing a common API. Maybe they are waiting to have all browsers on the same level before letting w3c evolve the spec.