Bamba made his plans known on The Players' Tribune on Thursday.
In his letter, the Harlem (New York) native said he bonded with Shaka Smart when he played under the Texas coach on Team USA (U18) last summer. He also said he admired the progress his friend Jarrett Allen, a projected first-round pick after a year at Texas, made last season.
"I can't say enough about the strides my friend Jarrett Allen made this past year," Bamba wrote. "I saw his footwork improve. I saw the spots they put him in -- where he was shooting, passing and stretching the paint like a modern 5. Most importantly, I saw his confidence grow throughout the season as he distinguished himself as a possible lottery pick. I'm thankful for the blueprint he laid down and I hope to follow in his footsteps."
Bamba, a McDonald's All American ranked third in the 2017 class, per ESPN.com, is the top recruit of Smart's tenure at Texas.
Bamba's arrival shifts the narrative at Texas, a program that underwent a turbulent 2015-16. Tevin Mack, the team's leading scorer last year, was suspended multiple times before he was dismissed. Mack announced his transfer to Alabama earlier this week.
Texas also lost Allen, and guard Andrew Jones will decide if he will return to Texas or remain in the NBA draft in the coming days.
But Bamba's arrival adds a 7-foot star to Smart's top-10 recruiting class, and proves -- despite last year's struggles -- that Smart is still one of the nation's strongest recruiters.
"I'm extremely excited that Mo has chosen Texas," Smart said in a statement. "He's as unique a person and player as I've been around. Mo's combination of talent, intellect and ability to impact others will make him a catalyst in our program and on our campus from day one."
ESPN's Jeff Borzello contributed to this report.