Pence and Davidson agreed to minor league contracts with invitations to spring training. Davidson is also expected to train for possible pitching duties with the club.
Pence, who grew up in Arlington, Texas, parted ways with the San Francisco Giants after the 2018 season. He spent seven seasons with the franchise and won two World Series titles (2012, 2014) and had an All-Star appearance during that span.
"He's got a long track record of being an elite teammate; a decorated, productive player on the field," Rangers general manager Jon Daniels told reporters. "From a standpoint of pedigree, makeup and way he goes about the game, it's consistent with the messaging of what we want this team to be about."
Offically signed with @Rangers today! Extremely excited for the opportunity! Can’t wait to get to work. I want to thank @whitesox and all the fans in Chicago for the past 5 years! Can’t forget to thank @Cut4 for the new headshots haha! pic.twitter.com/XOiNgtgFOL— Matt Davidson (@matt_davidson24) February 7, 2019
The 35-year-old Pence is a decorated 12-year MLB veteran, but struggled last season with the Giants. He was sidelined with a sprained right thumb from April 19 to June 1. He played in 97 games during the 2018 season and had a .226 batting average with four home runs and 24 RBIs.
For his career, Pence is batting .280 with a .334 on-base percentage and a .458 slugging percentage.
Davidson played in 123 games for the Chicago White Sox last season. He had a .228 batting average with 20 home runs and 62 RBIs. He also had three appearances as a pitcher and didn't allow a run across three innings pitched.