Alexander, a 6-foot-8 Curie senior who is regarded as a top forward in the 2014 recruiting class, announced he will join Bill Self's Jayhawks during a press conference at the high school. He chose them over DePaul, Illinois and Memphis.
Frontcourt players from Kansas have been selected in seven of the last nine NBA drafts.
"That played a big role," said Alexander, who said he finalized his decision Thursday night. "Me and my family talked about it and came to the conclusion that this is what I wanted to do."
Alexander said he probably will wait until January to sign his letter of intent.
He averaged 21.3 points, 13 rebounds and five blocks as a junior, when he led Curie to the class 4A sectional semifinals before losing to Young and top-ranked center Jahlil Okafor, who announced Friday he would attend Duke. Alexander said he and Okafor knew each other's selections before their respective announcements Friday and had discussed playing together.
Kansas big men Jeff Withey and Thomas Robinson were drafted the last two years after collegiate careers in Lawrence, Kan. Many NBA draft sites already project Alexander, who weighs 240 pounds, as a first-rounder for the 2015 draft.
Alexander said he would be one-and-done but would return to complete his education. Oliver, though, wasn't so fast to agree with the one-and-done statement.
"We don't want to put no number on years," Oliver said. "Whatever God's willing — one year, two years, three years. I think eventually he's going to reach his dream of being an NBA professional basketball player."
But Alexander first will have to earn his playing time on a team deep in the frontcourt. Six-foot-7 forward Kelly Oubre already signed his national letter of intent, and leading rebounder Tarik Black is among four Kansas forwards eligible to return next season. Reserve big man Jamari Traylor is a Chicago native.
"I'm ready to do whatever it takes to get to where I want to be," Alexander said.