The 21-year-old has penned an 18-month deal with the Millers – managed by former Whites head coach Neil Redfearn – with an option of another year.
Dawson becomes the third ex-Leeds player to join Rotherham this month following the earlier signings of Luciano Becchio and Alex Cairns.
Redfearn believes that he has signed an exceptional young talent in Dawson, who he nurtured through the Academy ranks at Leeds.
Redfearn, who admitted to be surprised that Leeds have let Dawson leave, said: “He is an exceptionally talented young player and on his day, he can unlock defences.
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“He’s a real plus for us.”
Dewsbury-born Dawson becomes the Millers’ second signing in the space of 24 hours and seventh so far in a hectic window following the capture of Birmingham’s Andrew Shinnie.
Fellow midfielder Chris Burke has also joined, along with striker Becchio and back-up keeper Cairns - plus defenders Aymen Belaid and Shay Facey.
Dawson was handed his debut by Neil Warnock in his final game in charge at Leeds on April 1, 2013.
Injuries have hampered Dawson’s development at times, but he was handed brief opportunities during Redfearn’s tenure as head coach at the club and was viewed as a long-term prospect with considerable potential - with the ability to step up to become a fully-fledged part of the first team squad alongside the likes of Alex Mowatt, Lewis Cook and Charlie Taylor.