The 40-year-old former Manchester City, Leicester and Blackburn player replaces Flynn, who stepped in after Dean Saunders left for Wolves and led the club to promotion from League One before taking up a senior role at the Keepmoat Stadium.
Dickov had been out of work since leaving League One side Oldham following a run of poor league form.
A statement on the Doncaster website said: "After extensive talks and interviews with various high quality applicants, Rovers' owners and chief executive Gavin Baldwin have concluded the search for a new manager and have confirmed that former Oldham Athletic manager Paul Dickov is the correct person to move Doncaster Rovers forward.
"An eighteen point criteria was set to identify the best possible candidate for the role. These criteria covered a whole range of aspects of the club in addition to the football.
"After completing the interview process, the board were in agreement that Paul was the best person to put their plans into action."
The former Scotland international believes his new side will be able to compete in the second tier.
"It's a challenge but a challenge I am going to embrace," he said.
"I am a very positive person and without setting any specific targets we will go into next season with momentum and a lot of confidence to do really well.
"I don't think we can put a ceiling on what we can achieve. It's a fantastic club with fantastic people, it's stable and that is something that I have been striving for.
"I could say that our aim is to stay in the division but I think that sends out a negative vibe straight away.
"You have got to set your bar high and you never know what you can achieve.
"Yes we are going to have to get players with a real good quality, but the feel-good factor is already there."
Dickov led Oldham to final positions of 17th and 16th in his two full campaigns at Boundary Park and also oversaw a shock victory over Liverpool in the third round of this season's FA Cup.
The former striker's playing career began at Arsenal and also included stints with Luton, Brighton, Crystal Palace, Blackpool, Derby and Leeds.