The 21-year-old, who worked with Millers boss Neil Redfearn at Leeds, was released by the Elland Road side on Wednesday after making four appearances for the club.
"I'm really happy and looking forward to a new challenge and a fresh start," he told the club website.
"It's an important year and a half in my career."
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Rotherham United have signed former Leeds United midfielder Chris Dawson on an 18-month deal.