The deal - which is pending a physical - will pay Happ $8 million, Jon Heyman of MLB Network reports.
Happ, 38, spent most of the last three seasons with the New York Yankees, with whom he primarily worked as a starter. He posted a 3.47 ERA, 4.57 FIP, and 1.05 WHIP with 42 strikeouts and 15 walks during the shortened 2020 campaign.
In Minnesota, Happ could slot in at the back of the rotation. Rich Hill filled the role last year.
The 14-year veteran has proved durable in the back half of his career, averaging 150 innings per year since 2015. Happ also has substantial postseason experience; he's pitched on six playoff teams and won a World Series as a rookie with the Philadelphia Phillies in 2008.