The deal was announced Tuesday. 3M will serve as the associate sponsor for Gordon's No. 24 Chevrolet in all other races from 2015-17.
3M had been on Greg Biffle's car for Roush-Fenway Racing.
Gordon is a four-time NASCAR champion, and his 90 victories rank third on the career wins list. He's second in the points standings, with two wins and 15 top-10s in 22 Sprint Cup races this season.
All five of 3M's business units, which comprise more than $31 billion in annual sales, will use the sponsorship in consumer promotions, product launches and business-to-business opportunities.