Patterson will formally be introduced as the replacement for DeLoss Dodds this week. Dodds is stepping down after 32 years.
"Steve Patterson emerged as the perfect candidate to build on Texas' athletic success and DeLoss Dodds' legacy," Texas president Bill Powers said in a statement. "Steve helped build an NBA championship team and brought the Super Bowl game to Houston. Far more important, he's run a winning program at Arizona State that places students first and is committed to their lifelong success."
The appointment is subject to approval from the UT System Board of Regents, which is scheduled to meet Nov. 12. The university said Patterson, if approved, would begin this fall.
Dodds, who will remain under contract until Aug. 31, 2014, oversaw an athletics budget of $163.3 million, the largest in the nation.
The 55-year-old Patterson, who has undergraduate and law degrees from Texas, had served as the AD at Arizona State since 2012. He also worked for the Houston Texans (1997-2003), Houston Rockets (1989-93) and Portland Trail Blazers (2003-07).
"During his stay at ASU, Steve Patterson has positioned Sun Devil athletics to continue its forward momentum well into the future," Arizona State president Michael Crow said in a statement. "I well understand his desire to return to his home state and wish him well at the University of Texas."
Patterson interviewed for the job over the weekend and emerged as the favorite over West Virginia athletic director Oliver Luck.
A source told ESPN's Brett McMurphy that Luck "thought he had it" as of Monday night but was told Tuesday that Patterson was getting the job.
Among the decisions that await Patterson will be the futures of football coach Mack Brown and basketball coach Rick Barnes. Brown, whose roller-coaster season has the Longhorns now eyeing the Big 12 championship after starting the season 3-2, is under contract until 2020 and will be paid $5.4 million this year.
Crow has appointed senior vice president James Rund as the interim AD at Arizona State while the school begins a national search.