The Nigerian has agreed a four-year deal with the npower Championship club, joining former Fulham team-mate Danny Murphy at Ewood Park.
Etuhu, 30, becomes Rovers boss Steve Kean's seventh signing of the summer as they prepare for life in the second tier following relegation from the Barclays Premier League last season.
The former Norwich and Manchester City man will join his new team-mates in Holland this weekend.
"Dickson is a player I have admired for a long time and he will be a fantastic addition to the squad," Kean told the club's official website, www.rovers.co.uk.
"He is a powerhouse in midfield who has played at the highest level with Fulham and we feel confident he will complement our other midfield options."