The 31-year-old forward, who had refused to play for the Whites to try and facilitate a move away from the club, was strongly linked with a move to Ewood Park during January but the dramatic sequence of events which engulfed Elland Road on deadline day put the deal on ice.
However, Rovers boss Gary Bowyer has finally got his man on a loan deal until the end of the season with a view to a permanent move.
"He is a great addition to the squad and a great lad," Bowyer told the club's official website.
"He has been very keen to join us. He works really hard, he is a great team player and gives us further options in our attacking areas.
"He is an aggressive forward who will give defenders a real handful."
Varney, who lists Crewe, Portsmouth and Sheffield Wednesday among his former clubs, goes straight into Blackburn's squad for the trip to Middlesbrough.