Matusz, a former first-round pick, played for the Orioles from 2009 until 2016.
The three-time Cy Young winner will turn 42 in February.
Bob Veale spent 11 seasons with the Pirates and helped lead the team to a World Series title in 1971.
Lux adds an above-average lefty bat to a Cincinnati lineup that needed a boost and clears some room in the Los Angeles infield.