The Merseyside giants will pay an undisclosed fee in compensation due to the player's age with the prospect of The Lions receiving additional payments should the youngster establish himself at Anfield or be sold on to another club.
The youngster was one of the stars of last season's run in the FA Youth Cup and his performances were to be rewarded with a professional contract this season.
"We're very disappointed to be losing David," manager Willie Donachie told the club's official website. "We believe he had the potential to become a first team player here and he would have turned professional with us on his 17th birthday.
"It is always a gamble for a young player to move to a big club at such a young age, but David's parents made it clear that the family felt it was the right move for him.
"My view is that if a player has the ability, the best way of reaching the top level is to gain valuable first team experience at an early age and then move on in due course."
However, the Millwall boss tried to remain upbeat about the move.
"We have a number of other exciting prospects in our Academy," he continued. "And I look forward to seeing them develop during the coming season."