Rovers sacked Gary Bowyer on Tuesday after a run of just one win in six games and currently sit 16th in the league.
The ex-Norwich City gaffer Lambert said: “I would like to thank the owners and Board of Directors for giving me the opportunity to manage such a fantastic club.
“Blackburn Rovers is a club with superb support and fine traditions, being a founding member of both the Football League and the Premier League.
“After a short period out of the game, I feel refreshed and I am really looking forward to the challenge ahead.
“I bring with me a very trusted backroom team that I believe is equipped to help me create an exciting era for the club and I hope to deliver a brand of football that will both entertain the supporters and bring success.”
The owners of the former English champions said of the appointment: “We are extremely happy to have secured a manager with the experience that Paul brings.
“We are confident that he is the right man to achieve the ambitions we have for the club.”