Former England international Murphy, 35, who signed a two-year deal at Ewood Park earlier on Monday, had several options following the expiry of his contract at Fulham but was persuaded by the resolute Kean, who remains determined to win over Blackburn's fans following relegation last month.
The club's Indian owners Venkys confirmed last week that Kean would still be in charge when Blackburn embark on their first season outside the top flight in 11 years.
Murphy, who has spent the last eight years in London with Charlton, Tottenham and Fulham, told Blackburn's official website: "I'm absolutely delighted to be signing for Blackburn Rovers.
"When meeting Steve Kean I soon realised the passion, enthusiasm and ambition he has for the club and how much he wants the team to bounce straight back up to the Premier League.
"His desire to get me to the club was a huge factor in my decision to join. The owners were also very passionate about their desire to move Blackburn forward as a club and create a squad that is able to achieve promotion.
"I'm excited about my new challenge and can't wait to get started.
"I have enjoyed a fantastic five years at Fulham and I'd like to thank the club and the fans for all their support.
"Now my new challenge is to help Blackburn get promoted and repay the manager's and the owners' faith in me."
Murphy began his career at Crewe before a £3million deal saw him move to Liverpool in the summer of 1997.
The midfielder won the FA Cup, League Cup twice and the UEFA Cup during seven seasons at Liverpool, but headed south to Charlton, who paid £2.5million for him in August 2004.
Murphy, capped nine times by England, moved to Tottenham for £2million in January 2006, but started only 11 games during an 18-month spell at White Hart Lane.
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In August 2007 he then moved on to Fulham, where he enjoyed greater success, racking up over 200 appearances for the Cottagers, who he helped reach the Europa League final in 2010 under now England manager Roy Hodgson.
Murphy is Rovers' first summer signing and boss Kean added: "Being able to bring Danny on board is a massive boost for everyone and I couldn't be more delighted.
"His record is there for all to see. He is a model professional, who has a real hunger to keep on playing football and we are thrilled he has decided to commit his future to us.
"This is a pivotal signing for us."