Steele, 36, has been at Xavier for 10 seasons, including the last two as associate head coach. He worked under Mack for nine of those seasons.
"As we completed our national search process, it became clear that the best head coach for our program is the person we knew the best, Travis Steele," athletic director Greg Christopher said. "Travis has impacted the Xavier basketball program in a variety of ways during his time at Xavier, whether in the office, on the court or in recruiting. Travis brings passion, personality and organizational leadership skills to our head coaching position, which is really the CEO of our basketball program. He has earned a reputation as one of the brightest young offensive minds in the game and one of the future stars in this profession."
Prior to arriving at Xavier, Steele spent two seasons at Indiana and one season at Wabash Valley College. The Indiana native has deep ties in the Midwest, including several seasons working with AAU and high school programs.
"I am excited about the opportunity to build on the success that we've enjoyed in the Xavier basketball program," Steele said. "I want to thank the Xavier administration and everyone involved in the search process, especially Greg Christopher."
With Steele on staff, Xavier went to nine NCAA tournaments and five Sweet 16s. The Musketeers won the Big East regular-season title and earned a No. 1 seed this season.
Steele replaces Mack, who left earlier this week for the vacancy at Louisville.