Embed YouTube video from custom field value

I’m collecting Youtube video links in custom fields, but when I echo out the value it just prints the URL. How do I get WordPress to convert it to be embedded?

Example:

<?php global $post;
$video = get_post_meta( $post->ID, '_my_video_link', true );
echo ( $video ); ?>

Just outputs http://www.youtube.com/watch?v=tkEvSjdDfiA

But I want it to display the actual video…

Thanks for any advice