The fee was undisclosed by the second tier English clubs but media reports said it was around nine million pounds.
Rhodes has agreed a four-and-a-half year contract, Middlesbrough said on their website (www.mfc.co.uk).
The 25-year-old marksman scored 85 goals in 169 appearances for Blackburn, including 11 this season, and netted 87 times in 148 outings for his previous club Huddersfield Town.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
Middlesbrough are second in the Championship. The top two go up to the Premier League automatically while the next four teams go through to the playoffs that yield one more promotion place.
(Writing by Tony Jimenez; Editing by Alan Baldwin)
