Sveum's son, Rustin, who was 5-1 pitching for Desert Mountain High School in Scottsdale, Ariz., was the pick.
"I called him, and he was watching the Draft, and I told him to just keep his eyes open, and he ended up getting drafted in the 39th round," Sveum said Wednesday at Miller Park. "He let out a big scream. It's one of those proud days. He's still got to develop. He better not sign -- he better go to college."
Rustin already has committed to Dixie State College in St. George, Utah. Asked if his son was represented by super agent Scott Boras, Sveum said no.
"He's a Sveum guy," the Cubs manager said.
Rustin, a switch-hitter, was drafted as a third baseman but has played mostly first base in high school. This year was his first as a pitcher. Sveum said his son was the No. 2 pitcher on the high school staff.
"He threw strikes and did his job," Sveum said. "He still has to develop physically."
Rustin has grown quite a bit. A year ago, he was 5-foot-7, and now he's 6-foot-1. He has the hand speed, and the athleticism is just starting to come around, Sveum said. Can he hit for power?
"No -- I think he will, I think he's got a chance," Sveum said. "He can hit the ball. Taking [batting practice] at [Miller Park], he hits it, from both sides of the plate, he hits home runs here. He's got the power. He didn't play a lot this year in the field, he pitched mostly, and had about 50 at-bats in high school."
There was no time to celebrate as Rustin had a doubleheader on Wednesday. He has high hopes to make it to the big leagues.
"It's something he wants to do," Sveum said. "He's got a lot of hard work [to do], and I think he understands how much goes into all this from being around here all the time.
"Whatever happens the next four years, you'll always be able to say you got drafted by the Chicago Cubs. It'll always be on your resume."
Carrie Muskat is a reporter for MLB.com. She writes a blog, Muskat Ramblings, and you can follow her on Twitter@CarrieMuskat. This story was not subject to the approval of Major League Baseball or its clubs.