"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."
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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
1981-1984: Patrick
1984-1986: Bass Brewers
1986-1987: Sportsweek
1987-1991: Maxwell Communications Corporation
1991-1995: Auto Windscreens
1995-1998: PUMA
1998-2001: EDS
2001-2005: Marston's Pedigree
2005-2008: Derbyshire Building Society