Homebrew を使ってwebp対応のffmpegをインストール

標準のバイナリでは、webp は有効になっていません。
Mac で ffmpeg ビルドするならば、以下のように、homebrew でできます。

brew install ffmpeg --with-fdk-aac --with-ffplay --with-freetype \
  --with-libass --with-libquvi --with-libvorbis --with-libvpx --with-opus \
  --with-x265 --with-webp

すでに、ffmpeg が入っている場合は、brew reinstallに置き換えてください。

以下のように、mp4 -> webp で animated な webpができます。

ffmpeg -i input.mp4 -vcodec libwebp -lossless 0 -qscale 75 -preset default \
  -loop 0 -an -vsync 0 output.webp

なお、brew install ffmpegで使えるオプションはbrew info ffmpegで確認できます。

$ brew info ffmpeg
ffmpeg: stable 3.1.2 (bottled), HEAD
Play, record, convert, and stream audio and video
https://ffmpeg.org/
/usr/local/Cellar/ffmpeg/3.1.1 (236 files, 51.5M)
  Poured from bottle on 2016-08-19 at 09:23:08
/usr/local/Cellar/ffmpeg/3.1.2 (241 files, 55.3M) *
  Built from source on 2016-08-19 at 10:30:23 with: --with-fdk-aac --with-ffplay --with-freetype --with-libass --with-libvorbis --with-libvpx --with-opus --with-x265 --with-webp
From: https://github.com/Homebrew/homebrew-core/blob/master/Formula/ffmpeg.rb
==> Dependencies
Build: pkg-config, texi2html, yasm
Recommended: x264, lame, xvid
Optional: faac, fontconfig, freetype, theora, libvorbis, libvpx, rtmpdump, opencore-amr, libass, openjpeg, snappy, speex, schroedinger, fdk-aac, opus, frei0r, libcaca, libbluray, libsoxr, libvidstab, x265, openssl, libssh, webp, zeromq, libbs2b, rubberband, zimg, xz, libebur128
==> Options
--with-faac
	Build with faac support
--with-fdk-aac
	Enable the Fraunhofer FDK AAC library
--with-ffplay
	Enable FFplay media player
--with-fontconfig
	Build with fontconfig support
--with-freetype
	Build with freetype support
--with-frei0r
	Build with frei0r support
--with-libass
	Enable ASS/SSA subtitle format
--with-libbluray
	Build with libbluray support
--with-libbs2b
	Build with libbs2b support
--with-libcaca
	Build with libcaca support
--with-libebur128
	Enable using libebur128 for EBU R128 loudness measurement
--with-libsoxr
	Enable the soxr resample library
--with-libssh
	Enable SFTP protocol via libssh
--with-libvidstab
	Enable vid.stab support for video stabilization
--with-libvorbis
	Build with libvorbis support
--with-libvpx
	Build with libvpx support
--with-opencore-amr
	Enable Opencore AMR NR/WB audio format
--with-openh264
	Enable OpenH264 library
--with-openjpeg
	Enable JPEG 2000 image format
--with-openssl
	Enable SSL support
--with-opus
	Build with opus support
--with-rtmpdump
	Enable RTMP protocol
--with-rubberband
	Enable rubberband library
--with-schroedinger
	Enable Dirac video format
--with-snappy
	Enable Snappy library
--with-speex
	Build with speex support
--with-theora
	Build with theora support
--with-tools
	Enable additional FFmpeg tools
--with-webp
	Enable using libwebp to encode WEBP images
--with-x265
	Enable x265 encoder
--with-xz
	Enable decoding of LZMA-compressed TIFF files
--with-zeromq
	Enable using libzeromq to receive commands sent through a libzeromq client
--with-zimg
	Enable z.lib zimg library
--without-lame
	Disable MP3 encoder
--without-qtkit
	Disable deprecated QuickTime framework
--without-x264
	Disable H.264 encoder
--without-xvid
	Disable Xvid MPEG-4 video encoder
--HEAD
	Install HEAD version
==> Caveats
The native FFmpeg AAC encoder has been stable since FFmpeg 3.0. If you
were using libvo-aacenc or libaacplus, both of which have been dropped in
FFmpeg 3.0, please consider switching to the native encoder (-c:a aac),
fdk-aac (-c:a libfdk_aac, ffmpeg needs to be installed with the
--with-fdk-aac option), or faac (-c:a libfaac, ffmpeg needs to be
installed with the --with-faac option).

See the announcement
https://ffmpeg.org/index.html#removing_external_aac_encoders for details,
and https://trac.ffmpeg.org/wiki/Encode/AAC on best practices of encoding
AAC with FFmpeg.