The 25-year-old is Dennis Wise's first signing as Whites boss and he goes straight into the squad for tomorrow's visit of Southend.
Stack began his career at Arsenal and has had loan spells at Belgian club Beveren and Millwall before joining Reading as cover for number one Marcus Hahnemann.
However, he only started one league game for the Royals and will now compete with Tony Warner and Neil Sullivan for the No 1 slot at Elland Road.
United have been undermined by defensive problems during the last two months with the backline conceding 20 goals in six matches prior to tomorrow's match.