Here is a full explanation:
ffmpeg -i image.jpg -i audio.mp3 -c:v libx264 -tune stillimage -c:a copy out.mp4
c:v libx264: use x264 to encode video.
tune stillimage: x264 setting to optimize video for still image encoding
c:a copy: copies the codec used for the input audio. You may change this if you want a different audio codec.
I did not use -loop 1 or -shortest. -loop 1 drastically slows down the encoding and creates a larger file. -shortest should not be used without -loop 1 since then the video will be one frame long. However YouTube does not like videos with one frame (see PJ Brunet’s answer) so then both options should be used.