The move comes a week and a half after the Cubs hired Carter Hawkins from Cleveland's front office as general manager to work under president of baseball operations Jed Hoyer.
Bokhari, 38, spent the past three years working in player evaluation for Houston. He oversaw all projects by the team's research and development group.
Bokhari's baseball career began in 2015 with the Los Angeles Dodgers. He spent four seasons in their research and development department.
Bokhari was a visiting assistant professor in the statistics department during the 2014-15 academic year at the University of Illinois, where he earned his master's degree in statistics in 2011 and doctorate in quantitative psychology in 2014.