The five-year deal with Yokohama Rubber Company eclipses the £18m-per-year-deal the club signed with Samsung in 2006.
Manchester United's seven-year deal with US car brand Chevrolet remains the biggest, worth around £50m per year.
Chelsea are top of the Premier League and are in the last 16 of the Champions League.
The West London club are now one of the world's most recognised sporting brands with an estimated 500m fans and were the most watched English side worldwide last season with 31,000 broadcast hours.
"Chelsea and Yokohama are a perfect fit. Both are global organisations with a focus on performance and innovation, as well as having huge ambition and an unwavering culture of success," Chelsea chairman Bruce Buck said on the club's website.
The Yokohama Rubber Company Ltd is a Tokyo Stock Exchange listed public company and deals in industrial, construction, marine and aerospace products, as well as golf equipment.
Its global business employs more than 20,000 people in over 120 countries, working across manufacturing, sales and servicing.
Chelsea have signed English football's second biggest shirt sponsorship deal - worth a reported £40m per year - with a Japanese tyre manufacturer.