nvEncodeAPI.h is nowadays hidden somewhere on nVidia's website and not quite as accessible as one would wish. However, due to its open license, that header file now is part of ffmpeg itself (nvenc.h in the libavcodec submodule). Just make sure you get some recent version of ffmpeg sources. I tried version 3.3.beta or something like that and it worked. Hopefully, most distributions will soon provide out-of-the-box NVENC support because of that.
apt-get build-dep ffmpeg
wget https://github.com/FFmpeg/FFmpeg/archive/master.zip
cd FFmpeg-master
./configure --enable-shared --enable-gpl --enable-libass --enable-libfreetype --enable-libx264 \
--enable-libx265 --enable-nvenc --enable-nonfree --enable-libfdk-aac --disable-static --disable-debug \
--prefix=/opt/obs-local --enable-cuda
make -j4
make install