Debian has switched to FFmpeg in testing in July but the work on the package did not stop at that point. After careful testing we can now provide official packages for Jessie users through jessie-backports. See installation instructions here. FFmpeg becoming available in jessie-backports also enabled us to provide Kodi from Debian in the same official repository.

Thanks to everyone in the Debian Multimedia Maintainers team, especially Andreas Cadhalpun who is also upstream developer at the FFmpeg project, Reinhard Tartler who maintained FFmpeg then Libav then FFmpeg again in Debian for long years and everyone else I could not name here but helped making this possible!