Davis hit .235 with 10 homers and 46 RBIs in 131 games with the Pirates after being acquired in an April trade from the New York Mets. The left-handed Davis served as part of a platoon at first base with right-handed Gaby Sanchez but found himself out of a job with the Pirates likely moving Pedro Alvarez to first in 2015.
Pittsburgh has 10 days to trade Davis or release him.
Taillon, the second overall pick in the 2010 amateur draft, missed the 2014 season after Tommy John surgery on his right arm.
Pittsburgh also added catcher Elias Diaz, infielder Pedro Florimon, outfielder Willy Garcia and pitcher Nick Kingman to its 40-man roster.