The deal, which is pending a physical, was first reported Monday by The Athletic.
Norris, 32, made 57 relief appearances and three starts for the Los Angeles Angels last season, going 2-6 with 19 saves and a 4.21 ERA. He struck out 74 batters in 62 innings.
Norris excelled in his role as the Angels' closer after having mostly worked as a starter in the majors. He finished 19-for-23 in save chances after collecting no saves in his eight previous major league seasons.
Selected by Houston Astros in the sixth round of the 2006 amateur draft, Norris made his big league debut three years later and was with the Astros until 2013, when he was traded to Baltimore for outfielder L.J. Hoes and a minor league prospect. He was 15-8 with a 3.65 ERA for the Orioles in 2014.