Matsui, a Japanese left-hander, has spent the past 10 years in Nippon Professional Baseball, where he made 236 saves in 501 career appearances for the Tohuku Rakuten Golden Eagles.
The five-time All-Star had a 2.40 career earned-run average in Japan with 860 strikeouts and led in saves in 2019 and the past two seasons.
Terms of the contract were not revealed but it reportedly pays Matsui $28 million with opt-outs after the 2026 and 2027 seasons.
Matsui, who also pitched for this year's Japan championship team in the World Baseball Classic, posted a 1.57 ERA this season with a career-best 39 saves and 72 strikeouts over 59 games.
The Padres have emphasized pitching in the off-season, bringing in four pitchers in a blockbuster trade deal with the New York Yankees for slugger Juan Soto.
San Diego's first off-season free agent signing comes two days after reports the Los Angeles Dodgers, a National League West division rival of the Padres had agreed to a 12-year deal worth $325 million with Japanese ace pitcher Yoshinobu Yamamoto.