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Leeds ended a 16-year wait to return to the top-flight after second-placed West Bromwich Albion's defeat at Huddersfield Town on Friday and were crowned champions of the second-tier Championship the following day when third-placed Brentford lost at Stoke City.
No financial details were disclosed but Leeds confirmed on Tuesday it was a record-breaking kit sponsorship deal for the club.
Adidas will take over from Italian sportswear brand Kappa, whose five-year deal with the club expires at the end of the current season.
"We're looking forward to our return to the Premier League with anticipation next season and partnering with adidas, who are one of the most recognisable names in sport, represents a new beginning for the club," said chief executive Angus Kinnear in a club statement.
Leeds host 21st-placed Charlton in the final game of the season on Wednesday.