Smith may be involved in the reserves' home game against Manchester United tomorrow night in Durham.
Leeds have confirmed the Edinburgh born youngster will move on a free transfer.
Smith has done well for Leeds reserves this season and impressed in their 2-1 win against Sunderland last month.
United's chief operating officer Shaun Harvey said on the official Leeds website: "We are delighted Kevin has been able to find another club. Leeds United wishes him every success in the future."
Smith becomes the second former Leeds Academy player to sign for the Wearside club, following Martin Woods' departure in July.