Wood was added to the Rangers' 40-man roster and optioned to Triple-A Round Rock.
The 28-year-old went 0-3 with a 5.63 ERA in 13 appearances for the Pirates this year. He was designated for assignment on Friday in order for the club to reinstate Ross Ohlendorf from the 60-day disabled list. He was released by the Nationals before the Pirates signed him to a Minor League contract on March 31.
When he wasn't with the Pirates from June 10-July 1, he was with Triple-A Indianapolis and posted a 2-0 mark with a league-leading 23 saves and a 2.84 ERA in 40 relief appearances.
He was 23-for-26 in save opportunities in the International League, holding opponents to a .196 batting average with just one homer, 12 walks and 32 strikeouts.
Selected by the Marlins in the 44th round of the 2002 MLB First-Year Player Draft, Wood is 1-4 with a 4.50 ERA over the course of 57 big-league relief appearances from 2009-11.