The 24-year-old decided to quit Norwich following their relegation to League One and joins on a free transfer as his contract was up.
The former Manchester City youngster is Nigel Clough's third summer signing, joining Jake Buxton and Ben Pringle in moving to Pride Park.
He told the club's official website: "I am delighted with this move and I can't wait to get started with pre-season training.
"Derby showed me their intentions early and showed how much they wanted me which was a big factor in me wanting to come here.
"Derby is a huge club with a great history and tradition, a tremendous support base and I feel there is a lot of synergy in both the club's and my ambition ."
Clough said: "This is a terrific capture for us and fills a position in the team where we need extra quality.
"Lee is an exciting talent who is proven at this level and above and has a great attitude.
"He has shown a great desire to play for Derby County as well and these are the types of players and characters I want at this football club as we look to progress and improve."