The teenage striker had been set to join Championship side Norwich City, but the Latics launched a last-minute bid for the player.
Manager Paul Jewell told the club's official website: "He is a player we have been monitoring for some time and we have decided to act now.
"David is one of those players who I think has the ability to make the grade in the Premiership, which is why we've decided to take him.
"He is very quick but he is also very hungry to learn and has a great attitude."