The defender enjoyed a week-long trial at Melwood earlier this month and seemingly did enough to earn a permanent move to the Premier League giants.
The Scotland Under-17 international will now continue his footballing education with the Reds' U23s, having made 11 appearances in the Scottish Championship this season.
Gallacher is the second player to depart Falkirk this month, joining Mark Kerr, 35, through the exit doors after his release.