Teagarden, 27, appeared in 118 games for Texas over the last four seasons, posting a .220 batting average with 16 home runs and 49 RBI. He has a .985 career fielding percentage and has thrown out 31 percent of runners attempting to steal.
"Taylor is an accomplished catcher who has shown an ability to handle a pitching staff and control the running game," said Orioles executive vice president of baseball operations Dan Duquette. "We believe he will be a nice compliment to Matt Wieters and our pitching staff and offensively he will provide good power."
In 14 games for the Rangers last season, Teagarden batted .235 and in 42 games for Triple-A Round Rock, he posted a .285 average with 12 home runs and 22 RBI.
To clear space on the 40-man roster for Teagarden, left-handed pitcher Pedro Viola was designated for assignment.
Henry, 21, appeared in 29 games between Class-A clubs Delmarva and Frederick in 2011, compiling a 4-3 record with a 2.22 ERA.