The 23-year-old, who scored 20 goals in 38 appearances last season, arrives at Pride Park on a four-year deal for an undisclosed fee thought to be in the region of £700,000.
Rams boss Nigel Clough, who has already brought in Burnley goalkeeper Lee Grant and Chris Martin from Norwich, had made Russell his top summer target.
"We're delighted to sign Johnny and his goalscoring exploits north of the border are something we've been aware of for some time," Clough said.
"He's been prolific in the last few years and from what we've seen of him we believe he can transfer that form to the Championship.
"At 23 he is a player who's only going to improve as well and we feel he's the right type of player to complement the options and players we already have in attack.
"We've had some stiff competition from a number of clubs to get him here so it's nice to come out on top and convince him Derby County is the best place for him.
"Johnny is an ambitious and hungry player and he shares our desire to be fighting it out for a top six spot next season and we're pleased to have him on board."
A product of Dundee United's youth system, Russell made his professional debut as a substitute during a 2-0 defeat to Falkirk in May 2007.
He had loan spells at Forfar and Raith Rovers before making his first-team breakthrough in the 2010/11 season.
"Would like to thank everyone at Dundee United who gave me the chance!" Russell wrote on Twitter.
"Really gonna miss the place, been the best 10 years of my life and met some great people! I wish United all the best in the future.
"Im absolutely delighted to sign for such a great club and can't wait for next season already!"