Update (8:45 PM EST): Rasmus will get a base salary in the range of $5 million with bonuses that can push it to around $7 million, according to Joel Sherman of the New York Post.
Rasmus, 30, had a down year with the Astros this past season. He finished batting .206/.286/.355 with 15 home runs and 54 RBI in 417 plate appearances. Rasmus had surgery in mid-October to repair his core muscle, shave down a bone spur, and repair the labrum in his left hip.
The Rays were looking for a cheap hitter who could handle corner outfield and some DH. Rasmus fits that bill. Given his career platoon splits — a .775 OPS against right-handers, .656 against lefties — the Rays may decide to use him in a platoon.