Rhoades, who will be introduced at a news conference Monday, is replacing Ian McCaw, who resigned on May 30amid controversy over the school's handling of sexual assault allegations.
Missouri said Wren Baker will serve as the interim AD and that the school plans to conduct a national search for Rhoades' successor.
"Baylor University is very pleased to welcome Mack Rhoades as Baylor University's Vice President and Director of Athletics," interim president David Garland said Wednesday in a statement. "He is a charismatic leader who pays careful attention to details and cultivates solidarity among the coaches and staff. He intends to build champions on the field and on the court and to mold student-athletes into champions in their lives after sports. Most importantly, he is committed to and excited by Baylor's Christian mission and vision."
The 50-year-old Rhoades took the AD job at Missouri in March 2015, replacing longtime AD Mike Alden and overseeing an athletic department budget of $92 million. Prior to that, Rhoades was the AD at the University of Houston since 2009.
"The past year has taught me a great deal about who I am as a person and as a leader," Rhoades said in a statement released by Baylor on Wednesday. "I am very grateful to the people I've worked with and come to know throughout the state of Missouri. The experience has helped galvanize a commitment to my core values and to the values I want to infuse into an athletics program."
His stint at Missouri came during a tumultuous period for the Tigers. University president and chancellor R. Bowen Loftin announced his resignation in November amid criticism of their handling of student complaints about race and discrimination.
Football coach Gary Pinkel resigned at the end of the 2015 season due to health issues, and Rhoades promoted defensive coordinator Barry Odom to replace Pinkel.
"In college athletics, it's very seldom that you get to work for the same guy for a number of years and we never know when it's going to happen, hopefully it never does," said Odom, who added that he had talked with Rhoades on Tuesday night about the move. "That's life. I'm pretty confident in what we're going to do as a football program and look forward to leading us the right way. ...
"Guys are presented different opportunities and they have to make the best decision for what's best for them. I feel good about Mizzou and where we're headed."
Missouri softball coach Ehren Earleywine is the subject of an ongoing internal Title IX investigation for allegations of verbally abusing players.
Additionally, Missouri's men's basketball program is coming off a self-imposed one-year postseason ban after a 19-month investigation of former coach Frank Haith and his staff uncovered several NCAA rules violations.
Rhoades will bring a familiarity with the landscape in the state of Texas to his job at Baylor. In addition to previously serving as AD at Houston for almost six years, he also worked at UTEP for seven years before becoming AD at Akron in 2006.
"I look forward to the opportunity to join Baylor University at this important time in its history," Rhoades said in the statement. "I am excited to support and develop programs of the highest caliber, in facilities that are second to none, alongside coaches who are among the best in the industry, all grounded in a Christian tradition and committed to academic excellence."
Houston moved to the American Athletic Conference, raised nearly $100 million and built $160 million worth of new facilities during Rhoades' tenure, including the on-campus TDECU Stadium for UH football. He was also responsible for hiring football coach Tom Herman, who led the Cougars to a 13-1 2015 season and Peach Bowl victory in his first year.
McCaw, who had served as Baylor's athletic director since 2003, had been sanctioned and put on probation as part of the school's response to the findings of the independent Pepper Hamilton investigation. He elected to resign rather thanbeing retained to help implement the recommendations that came with that report and restore accountability and oversight to the athletic department.
Baylor's program has been rocked by allegations of sexual assault and other violence involving several players. As a result, the board of regents suspended former football coach Art Briles with intent to terminate and stripped chancellor Kenneth Starr of his title of university president.
Former Wake Forest coach Jim Grobe is currently the Bears' interim football coach.
ESPN staff writers Max Olson and Edward Aschoff contributed to this report.