Clement will take up his position immediately and replaces John Jensen, who left Steve Kean's coaching staff at the end of last month.
The 39-year-old Clement has had two spells at Chelsea, including being the assistant first team coach to Carlo Ancelotti, and also spent seven years at Fulham and three years as the Republic of Ireland Under-21 coach.
Clement, who left Chelsea this summer, told Blackburn's official website: "I'm excited to be here at a big club like Blackburn Rovers and am really looking forward to the challenge.
"It's great to be linking up with Steve again, having worked with him previously at Fulham, and I can't wait to get started."
Kean added: "I'm delighted that Paul has agreed to join us. He is someone I know well and respect as a coach and will be on the bench with me at QPR tomorrow."
Blackburn are second-bottom of the Premier League standings heading into their trip to QPR having picked up four points from their opening seven games.
Clement, who has signed a rolling contract, is looking forward to his first competitive match with his new club - back in the same area of London which has so many family ties for him.
"It is funny my first fixture is right back to where I came from, just up the road from my old club," he added.
"I was a QPR supporter growing up and my dad (Dave) played there for 10 years so I am really excited about the game tomorrow.
"My role at Chelsea ended in the summer - it was a fantastic experience there and I look back on it with fond memories - but you move on because that is the life of a football coach."