Lamb, 26, was designated for assignment by Cincinnati on Oct. 27, three days after he underwent back surgery for the second time in as many years. He was out of Minor League options and not expected to be ready until well into the 2017 season.
The Reds acquired Lamb, along with lefty pitchers Brandon Finnegan and Cody Reed, from the Royals for ace Johnny Cueto on July 26, 2015.
Lamb's value diminished as he went 2-12 with a 6.17 ERA in 24 big league starts over parts of the past two seasons.