The message comes approximately three weeks after Kaprizov declined a first offer, it was about an eight-year contract worth 120 million kronor, also a record.
The contract applies from and including next season and until 2034 and Kaprizov, 28, will earn an average equivalent to 160 million kronor per season.
This is the highest seasonal salary since the salary cap was introduced in the NHL in 2005. Edmonton's Leon Draisaitl had the previous record with a salary of equivalent to almost 132 million kronor per season.
Kirill Kaprizov came to the NHL and Minnesota in 2020 and has made 386 points (185 goals + 201 assists) in 319 regular season matches.
The 28-year-old forward made the decisive goal in overtime in the Olympic Games final 2018 in South Korea when the Russian team, which went under the name OAR (Olympic athletes from Russia), took the gold.
Russia is suspended from international ice hockey and may not participate in the Olympic Games in Milan due to the war of aggression against Ukraine.
Correction: In an earlier version, it was stated that Auston Matthews had the highest salary previously, the correct one should be Leon Draisaitl.