Harrison, the club's pitcher of the year in 2012, is the fourth Opening Day starter for Texas in the last four seasons.
Harrison went 18-11 last season with a 3.29 ERA and earned his first trip to an All-Star Game.
Yu Darvish, also an All-Star last season, will start the April 2 game against Houston.
The Astros announced their rotation for the three-game series on Wednesday. Houston will start Bud Norris opposite Harrison. Lucas Harrell will start opposite Darvish and Phillip Humber in the series finale. The Rangers haven't announced their rotation plans past Darvish.
Harrison is 0-1 against Houston with a 5.14 ERA in four appearances.