Al Ekhbariya added the contract with Kante, who won the 2018 World Cup with France, has an option to be extended for another year.
A source close to Argentina captain Lionel Messi (35) last month told Reuters that he had received a formal offer to join Al-Hilal. However, the World Cup winner looks set to join Inter Miami in the United States.
Kante's deal is worth 100 million euros over two years, Saudi media said.
The France international has been a mainstay at Stamford Bridge, making more than 260 appearances and winning the Champions League, Premier League, Europa League and FA Cup during his seven years at the club.
Kante's last season was plagued by injuries, however, as he missed the majority of the campaign. Chelsea struggled without him to finish 12th in the Premier League standings.