Per Encina, the O's have been in search of a left-handed hitting outfielder throughout free agency, and Rasmus fits the bill.
The 31-year-old Rasmus was productive in 37 games last season, hitting .281 with nine home runs and 23 RBI in his first season with Tampa.
He has four seasons with 20 or more home runs, and in nine MLB seasons, Rasmus owns a .242 average with 165 homers and 490 RBI.
Baltimore has a strong lineup, but it is heavy on right-handed hitters, including Manny Machado, Adam Jones, Jonathan Schoop, Trey Mancini and Mark Trumbo.
Rasmus would help balance the lineup and create a potential outfield platoon with Joey Rickard, while Jones and Mancini occupy the other two spots.