The 24-year-old striker, who scored 25 goals last season, recently penned a two-year extension at Ewood Park.
Rhodes had been linked with a move to Championship rivals Norwich City before committing himself to Rovers last week.
"I think it's good for the team and for the club that he's put pen to paper," Cairney told the Lancashire Telegraph.
"He's scored 50-odd goals in two seasons and when you've got a talisman like that you want to keep him. I think I speak on behalf of the boys when I say that we are all very happy he has signed."
Blackburn begin the new Championship season at home to Cardiff City on August 8.