McCullers, who has committed to play for the University of Florida, is 6-foot-2 and weighs 205 pounds. He is the son of Lance McCullers Sr., who was a reliever in the Majors from 1985-92.
McCullers might have slipped in the Draft due to signability concerns. He is represented by agent Scott Boras and is considered to have a firm commitment to Florida.
Luhnow, who wants to keep McCullers a starter, said the Astros contacted the right-hander's representatives before making the selection to make sure they were on the same page. The Astros felt comfortable with the answer they received.
"I believe that we will sign Lance McCullers and he will be a Houston Astro," Luhnow said.
Luhnow joked that he won't be popular among college programs in Florida after taking McCullers and using the No. 1 overall pick to select shortstop Carlos Correa, who has committed to the University of Miami.
"I'll have to keep my head down during Spring Training," Luhnow said.
The 41st pick has a bonus pool value of $1.258 million, and the signing bonus cap for Correa is $7.2 million. The Astros have a total bonus pool of $11.177 million, the second highest in the Majors. Houston has until July 13 to sign its selections.
McCullers' fastball ranges from 94-96 mph but has touched 100 on occasion. He also throws a slider, a curveball and a changeup.
"He's got not just a pretty good fastball," Luhnow said. "He's got one of the best fastballs in the country."
Last season at Jesuit, McCullers went 13-0 with a 0.18 ERA, striking out 140 and walking 30 in 77 1/3 innings. He also hit .280 with 27 runs scored and 21 RBIs.
"His numbers in high school competition in Florida, which is pretty good competition, speak for themselves," Luhnow said. He's going to quickly become one of our top pitching prospects."
The Astros received the 41st pick after infielder Clint Barmes signed with the Pirates this past offseason.