Krause has been in his current position for less than a year. The White Sox were counting on him to restore their presence in Latin American countries after former team executive Dave Wilder and two scouts were allegedly involved in a scheme to skim money off players' signing bonuses.
Krause, a former Chicago Bulls general manager, will serve as the Diamondbacks' special assistant to Jerry DiPoto, executive vice president of scouting and player development. Krause has been involved in baseball scouting for 21 years.
He ultimately will be a special assistant involved with scouting, including evaluating the Diamondbacks organization.
The Chicago Tribune first reported the move.
Doug Padilla covers the White Sox for ESPNChicago.com and ESPN 1000. ESPNChicago.com's Bruce Levine contributed to this report.