Slew has made only two appearances since joining Rovers in August 2011, and a six-month loan spell at Oldham this season was curtailed when he suffered a back injury.
But Millers boss Steve Evans has been impressed with what he has seen of the 20-year-old, and he is delighted to have him on board.
"Jordan is a young man who I have seen produce a number of outstanding performances," said Evans.
"I have landed him after asking the question to a number of recent Blackburn Rovers managers. Thankfully Michael Appleton has sanctioned the move.
"I watched Jordan on a number of occasions whilst he was on loan at Stevenage last season and on those occasions I watched him live, he was by far the best player on the pitch.
"He is young, has explosive pace, is powerful and has a real work-ethic which I'm sure will see the Millers support take to the lad.
"It has been a long search to land a striker of this quality and he will be on the training ground with us in the morning as we prepare to face the in-form team in League Two, Northampton Town."