Henry gives the Red Sox some depth at the upper-Minor League level. Last year at Triple-A Toledo, the 27-year-old hit .300 and stole 22 bases.
The Sox also lost a prospect at the outset, as the Astros took right-hander Josh Fields with the No. 1 pick in the Rule 5 Draft.
"He's a good pitcher," said Red Sox director of professional scouting Jared Porter. "We like to keep everybody."
Drafted by the Mariners in the 2008 First-Year Player Draft, Fields had been with the Red Sox's organization since coming over with Erik Bedard at the July 31 non-waiver Trade Deadline in 2011.
Fields split the 2012 season between Double-A Portland and Triple-A Pawtucket, going 4-3 with a 2.01 ERA in 42 games, all in relief.
The Red Sox also lost righty Ryan Pressly to the Twins. Pressly was drafted by Boston in the 11th round in the 2007 First-Year Player Draft. He was 7-5 with a 5.38 ERA in 2012, splitting the year between Class A Salem and Double-A Portland.
"He's always had a good arm. He has good stuff. Good fastball and curveball," Porter said.
The Sox added a local product, taking left-hander Jack McGeary in the Triple-A portion of the Draft from the Washington Nationals. McGeary was born in Boston and went to high school at Roxbury Latin.
"He missed some time, had Tommy John urgery, but he's a year and a half to two years removed from that," said Porter. "He's a good kid with good makeup. He's a lefty with good command. His fastball is up to 91 [mph]. [His] secondary stuff is still a work in progress. Good delivery."