"We are absolutely delighted," said Derby County managing director Mike Horton, "as adidas is a brand renowned for quality and that will appeal to our fans.
"This is a tremendous opportunity for the club and adidas to work together, and marks the start of what should be a long and rewarding relationship."
Gavin Thomson, sales director, adidas area north, said: "We are very excited about our new relationship with Derby County. This comes at an exciting time in Derby's own development."
Top Premiership clubs Chelsea and Liverpool wear adidas.
Next season's Rams replica kit, made by adidas, could be available to fans from August.
Shirt sponsors history
1884-1980: No sponsor
1980-1981: British Midland
1984-1986: Bass Brewers
1987-1991: Maxwell Communications Corporation
1991-1995: Auto Windscreens
2001-2005: Marston's Pedigree
2005-2008: Derbyshire Building Society