The former Aston Villa and Norwich City boss will be joined at Ewood Park by ex-Rovers player and youth team coach Alan Irvine as his assistant.
Rovers’ former head of youth coaching Rob Kelly and goalkeeping coach Laurence Batty will also be part of the new-look backroom team.
The new manager will be presented to the media on Monday.
Paul 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.”
Blackburn Rovers' Owners said: "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."