Debian Wheezy for Raspberry Pi comes with FFMPEG, however, the version installed by apt-get isn't compiled to use the native GPU driver so FFMPEG needs to be recompiled to use it.
Compiling on Raspberry Pi takes a while. If you cannot wait do cross-compiling
I added heatsinks the Raspberry Pi. Maybe a fan would also be a good idea.
apt-get install autoconf libtool checkinstall libssl-dev libmp3lame-dev
cd /opt wget http://tipok.org.ua/downloads/media/aacplus/libaacplus/libaacplus-2.0.2.tar.gz tar -xzf libaacplus-2.0.2.tar.gz cd libaacplus-2.0.2 ./autogen.sh --with-parameter-expansion-string-replace-capable-shell=/bin/bash --host=arm-unknown-linux-gnueabi --enable-static make make install
cd /opt git clone git://git.videolan.org/x264 cd x264 ./configure --host=arm-unknown-linux-gnueabi --enable-static --disable-opencl make make install
cd /opt git clone http://git.chromium.org/webm/libvpx.git cd libvpx ./configure make checkinstall --pkgname=libvpx --pkgversion="1:$(date +%Y%m%d%H%M)-git" --backup=no --deldoc=yes --fstrans=no --default
cd /opt git clone git://git.ffmpeg.org/rtmpdump cd rtmpdump make SYS=posix checkinstall --pkgname=rtmpdump --pkgversion="2:$(date +%Y%m%d%H%M)-git" --backup=no --deldoc=yes --fstrans=no --default
cd /opt git clone --depth 1 git://git.videolan.org/ffmpeg cd ffmpeg ./configure --arch=armel --target-os=linux --enable-gpl --enable-libx264 --enable-nonfree --enable-libaacplus --enable-librtmp --enable-libmp3lame make make install ldconfig
ffmpeg -version ffmpeg version git-2015-02-27-a220322 Copyright (c) 2000-2015 the FFmpeg developers built with gcc 4.6 (Debian 4.6.3-14+rpi1) configuration: --arch=armel --target-os=linux --enable-gpl --enable-libx264 --enable-nonfree --enable-libaacplus --enable-librtmp --enable-libmp3lame libavutil 54. 19.100 / 54. 19.100 libavcodec 56. 26.100 / 56. 26.100 libavformat 56. 23.106 / 56. 23.106 libavdevice 56. 4.100 / 56. 4.100 libavfilter 5. 11.102 / 5. 11.102 libswscale 3. 1.101 / 3. 1.101 libswresample 1. 1.100 / 1. 1.100 libpostproc 53. 3.100 / 53. 3.100