"Les Reed and Mark Robson will step up and run the team," Varney told Sky Sports News.
"We are probably looking for a third person to come in and help them. We feel we need stability more than ever.
"They are both Charlton people and have a very strong Charlton pedigree. We've very, very confident they will start to turn this club around.
"We think he's an exceptional coach with a wide range of international experience. We think they make a good team.
"One thing we do know is they are committed to turning things around here.
"We want to give them the opportunity. We hope they succeed."
Varney has rejected the suggestion that Charlton dismissed Dowie after panicking at the club's poor start to the Premiership season.
"We had to do something and we had to act to remedy the situation and that's why we have terminated Iain's contract," he added.
"(The fans) have to trust us. We've been here a long, long time. They know how the club is run.
"The board would not take hasty decisions if they did not feel it was in the best interests of the club. This is not a panic measure."