The diminutive 21-year-old was released by the Elland Road club on Tuesday and Millers boss Neil Redfearn has moved quickly to snap up the player he knows well.
Dawson is a player Redfearn brought through the ranks at Leeds and also played him three times for the first team last season.
He signs at the Millers on an 18-month deal and could be involved in Saturday's clash with Charlton at New York Stadium.
Redfearn said: "The big thing we have got to think about the bigger picture and we have got to plan and get strength in depth and have competition for places and have youth and young players coming through - and obviously Chris fits into that category.
"He is an
exceptionally talented young player and on his day, he can unlock defences. He
plays 10, off the front and wide and the thing with Chris and what has gone
against him in recent times is his size.
"He's 5ft 6in, but he's a player who
has real tenacity and strength and mobility and low sense of gravity to deal
with possession. He's a real plus for us."
Dawson is the third player who came through the Leeds ranks under Redfearn to join the Millers following the arrivals of Alex Cairns and Simon Lenighan.
