The 25-year-old left-hander, 4-2 with a 2.57 ERA in six starts last year after he recovered from elbow surgery, will be opposed by Seattle's Felix Hernandez in the April 1 matchup at Oakland.
Anderson said manager Bob Melvin gave him the news a day earlier.
"It sounded like he wanted to hug, but I am not going to jump up and down and things like that," the pitcher said. "If he wants one I'll give him one, but I won't go out of my way."
Anderson struck out one and walked none in his first outing of spring training.
"I was healthy, so that is step one, whether I gave up eight runs or zero like I did today," Anderson said. "It was good to continue to get ground balls on early contact. I felt good and threw my pitches for strikes."
Melvin said Anderson's dedication during rehabilitation last year is an indication of what a No. 1 starter is about.
"Based on the guys that we have and how successfully he came back for us last year, we really feel like he's the man to lead the staff," Melvin said. "He worked hard to get back and put himself in a position to compete with us at a time of the season where there's no easing into things. You got to be good right away, and he was. Then he gets hurt (oblique) and we think he's done, and he works just as hard to get back and pitch in a playoff game."
In his first appearance for the Cubs after leaving Texas as a free agent, Scott Feldman gave up one run and two hits in two innings with two strikeouts and two walks.
"It got the butterflies going again and it was nice to get that one out of the way," Feldman said. "For the most part, I was executing my pitches fairly well. For the first time out it was fine."
Darnell McDonald had two hits for the Cubs, including an RBI double in the fifth against Jordan Norberto. Cuban prospect Jorge Soler had a single and showed off his arm when he threw out the A's Josh Reddick at third base from right field in the first inning.
"That was about as good of throw as you can make," Feldman said. "I think Reddick kind of had a look of shock on his face."
A's closer Grant Balfour (right knee) was scheduled to see a doctor Thursday. He made 35 throws from flat ground on Wednesday, and his next step could be throwing off a mound. ... Cubs RHP Matt Garza (lat muscle) threw for 15 minutes from up to 60 feet. Friday is expected to be a day off before he throws again on Saturday. ... Cubs SS Starlin Castro said he was fine Thursday, but he is expected to miss two to three games after feeling tightness in his left hamstring in the fourth inning of Wednesday's game.