Bates, who had held the same post at Miami-Ohio since 2002, succeeds Gene DeFilippo, who retired after 15 years in the job.
"I am delighted that Brad Bates will be our next director of athletics," Boston College President William P. Leahy said. "He is thoughtful, a proven leader, and someone who understands and supports Boston College's commitment to excellence in both academics and athletics. I look forward to working with him."
At Miami-Ohio, the 53-year-old Bates presided over a program in which 14 of its 18 teams won at least one conference championship.
Bates, a Michigan graduate, also spent 17 years at Vanderbilt University.
"My wife Michele and I are honored to have this tremendous opportunity, and we feel an enormous sense of responsibility to the students, faculty, staff, alumni and fans of this extraordinary institution," said Bates. "Boston College offers a world-class education with first-rate athletics in one of the nation's best cities, and its Jesuit, Catholic tradition demands that we seek knowledge in ways that better the human condition and promote student development."