This can be done through the youtube player API:
Working example:
<div id="player"></div>
<script src="http://www.youtube.com/player_api"></script>
<script>
// create youtube player
var player;
function onYouTubePlayerAPIReady() {
player = new YT.Player('player', {
width: '640',
height: '390',
videoId: '0Bmhjf0rKe8',
events: {
onReady: onPlayerReady,
onStateChange: onPlayerStateChange
}
});
}
// autoplay video
function onPlayerReady(event) {
event.target.playVideo();
}
// when video ends
function onPlayerStateChange(event) {
if(event.data === 0) {
alert('done');
}
}
</script>