Allen, a standout at nearby Austin (Tex.) St. Stephen's Episcopal, was recruited by a host of high majors, but ultimately chose Texas over Houston and Kansas.
The Texas athletic department wasn't reached when asked for confirmation.
A 6-foot-10 center, Allen is regarded as the No. 3 center and No. 15 overall recruit in the 2016 recruiting class.
Allen, who played with Texas Pro on the spring and summer circuit, was selected to play in the McDonald's All-American game, as well as the Nike Hoop Summit, following a successful senior season.
With the addition of Allen, Texas has a pair of five-star prospects headed to Austin (Tex.). Allen joins Andrew Jones, as well as four-star prospects James Banks and Jacob Young to make up their 2016 class.
The commitment bumps Texas' class up to No. 6 in Scout's top 25 class rankings.