The former Sheffield United youngster, who signed for Rovers in 2011, will stay at New York until March 5, though the deal could be extended.
The signing brings Millers boss Steve Evans' long search for a frontman to an end and he is expecting big things.
"Jordan is a young man who I have seen produce a number of outstanding performances," Evans said.
"I have landed him after asking the question to a number of recent Blackburn Rovers managers. Thankfully Michael Appleton has sanctioned the move.
"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."
The 20-year-old will train with his new team-mates on Friday and could be in line to make his debut against Northampton on Saturday.