Tomasson has signed a three-year deal at Ewood Park alongside assistant coach Remy Reijnierse and fitness director Ben Rosen.
The Dane's appointment ended the club's search for a manager after Tony Mowbray departed last month when his contract expired.
Most recently, Tomasson managed Swedish side Malmo, leading them to back to back Swedish top-flight titles in 2020 and 2021 and the group stages of the Champions League, before leaving his post.
Former striker Tomasson, will be remembered for a stint at Newcastle in 1997 before a three-year spell at AC Milan.
He also had spells in Germany, Spain and Holland whilst boasting a record 52 goals in 112 games for Denmark.
After retiring in 2011, Tomasson took up coaching and had short spells as head coach of Dutch clubs Excelsior and Roda JC, before sealing assistant manager roles with Vitesse Arnhem and the Denmark national team.
"I'm really proud and excited to be taking over as Head Coach of Blackburn Rovers - a club with a lot of tradition and also great ambition," Tomasson told the club's official website.
"We have a young team here, and also a great Academy, and the Owners have a clear vision, which is to develop players and become a sustainable Premier League club over time, so I'm really happy to be involved in this exciting new chapter for the club.
"Since leaving Malmo, I have been looking for the right club and I had a lot of options, but after speaking to Steve and Gregg I got a really good feeling about the club and I knew that I had found my next opportunity.
"I grew up watching English football, so I know all about the passion for football here and how special football fans are in England, so it's great to come to such a big club as Blackburn Rovers and to be involved with such passionate fans and in a really good league, which the Championship is. It will be a great challenge, but it's something I'm really looking forward to being a part of."
Rovers ended the Championship season in eighth position, six points off the final play-off spot.