Texas plays the Astros in Houston on March 31 on ESPN at 8:05 p.m. ET. The Astros already have announced Bud Norris will pitch the opener for them.
Yu Darvish will start the Rangers' second game of the season in Houston on April 2.
"It's awesome," Harrison said. "To be starting Opening Day and to be among the guys that we have on this staff, is pretty cool and something I won't take lightly or for granted because it may never happen again."
The Rangers like to reward their best starters from the previous season, and Harrison was 18-11 with a 3.29 ERA in 213 1/3 innings (32 starts) in 2012. It was his second consecutive season with an ERA of less than 3.40 and at least 185 innings pitched. He signed a five-year, $55 million contract extension in the offseason.
"He was the most deserving guy after last season," Washington said. "I thought he was most deserving of this opportunity. He was excited and it was something he wanted, but he wasn't going to ask for it."
Darvish, acquired last offseason through the posting system for Japanese pitchers, was 16-9 with a 3.90 ERA in 191 1/3 innings (29 starts). He finished the season with a 5-1 record and a 2.35 ERA in his last eight outings -- all quality starts.
Washington said Darvish was "professional" about Harrison getting the start.
Darvish pitched a bullpen session Thursday and reported no problems. He is scheduled to start on Saturday against Cincinnati.
The 26-year old was scratched from his last scheduled start on Monday with a stiff neck he suffered during a workout the previous day. He also pitched a bullpen session on Tuesday.
Harrison pitched in a minor league game in Surprise on Thursday and allowed one run on four hits with no walks in six innings.
Left-hander Martin Perez will have the fractured ulna in his left forearm examined by team doctors on Saturday. Perez is no longer wearing the large, hard brace, which immobilized his lower arm since March 3, when he suffered the injury after being hit by a line drive. He has been wearing a soft, expandable brace since Monday.
"It feels good," Perez said. "When I move it, I don't feel anything. It feels normal."