The 31-year-old has moved to Ewood Park for the rest of the season, with Blackburn having the option to make the move permanent at the end of the campaign.
The deal was finalised in time for Varney to make the bench for Saturday's game against Middlesbrough.
Blackburn are chasing a play-off place in the Championship and Bowyer believes Varney will boost his side's promotion hopes.
"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 joined Leeds from Portsmouth in 2012.
'I think everybody has said something about it, so why should I add to it? It's so obvious that it's not necessary for me to' Everything that Liverpool boss Arne Slot said about James Tarkowski's unpunished horror tackle
Gary Lineker unveiled as FourFourTwo's latest cover star - we sat down with the legend of football and broadcasting to discuss his future after BBC Match of the Day
