The 33-year-old right-hander will receive $2 million next season. The White Sox hold a $3 million option for 2017 with a $250,000 buyout under the terms of the deal announced Thursday.
Albers made Chicago's opening day roster after being invited to spring training last season and went 2-0 with a 1.21 ERA in 30 appearances. He was on the disabled list from April 20 to July 15 with a broken right pinky finger.
Albers is 27-31 with a 4.20 ERA over 10 seasons with Houston (2006-07, `14), Baltimore (2008-10), Boston (2011-12), Arizona (2012), Cleveland (2013) and the White Sox.