David Wilder, 50, of San Francisco, pleaded guilty to one count of mail fraud as part of a plea agreement, telling a federal judge in Chicago, "I understand what I have done."
Prosecutors said he and two others were supposed to pay signing bonuses matching each player's skills but instead fraudulently inflated the amounts and took the additional money for themselves.
In a statement, the White Sox said they were pleased Wilder "will face responsibility for his crimes."
"But we also remain saddened by the betrayal of trust, the involvement of innocent players, the abuse of the system, and the impact his criminal actions inflicted on this organization," the team said.
Wilder faces up to 20 years in prison, but his plea deal will likely mean a less severe term. He was not taken into custody after the hearing and no sentencing date has been set.
Attorney Thomas Bienert Jr. told reporters after the hearing that his client is remorseful.
"He apologizes to the White Sox and any others that he harmed," Bienert said.
Wilder and two former scouts for the team in Latin America of accepting about $400,000 to secure 23 prospects between 2004 and 2008, according to the indictment handed down last year.
The White Sox at the time were recruiting in the Dominican Republic, Mexico, Panama, Venezuela and other Latin American nations, though the kickbacks were concealed from the team and its senior official, the indictment said.
Former scouts Jorge L. Oquendo Rivera and Victor Mateo also face mail fraud charges.
The mail fraud counts alleged that checks ranging from $30,000 to $525,000 were sent from the White Sox to players or teams for the contract rights to players.
Robert Grant of the FBI's Chicago office accused Wilder and the two other allegedly involved of trying enriched themselves by taking advantage of vulnerable ballplayers, who were anxious to pursue their dreams of stardom in the major leagues.
Oquendo, of Aguadilla, Puerto Rico, pleaded not guilty in November. A warrant has been issued for the arrest of Mateo, of Arroyo Hondo in the Dominican Republic.
An investigation into the matter began after the White Sox reported internal findings to Major League Baseball, and baseball officials then contacted authorities, the indictment says.
The White Sox in 2008 fired Wilder as director of player personnel and Mateo as a scout. The team offered few details at the time, saying only that the dismissals were "for actions in Latin America that were violations of club policy and standards."
Wilder began his player-development career with the Oakland Athletics in 1990 after a seven-year minor league career the Oakland and Cubs systems.
He was assistant director of scouting and player development for the Atlanta Braves from 1991-95; farm director and assistant general manager with the Cubs from 1996-99; and vice president of player personnel and special assignment scout with the Milwaukee Brewers from 2000-03, before joining the White Sox late in 2003.
He oversaw Chicago's entire minor league department and player development staff as well as the club's Latin American operations.
Wilder was also a member of the United States Olympic Baseball team's selection committee in 2000, helping assemble the team that won the gold medal.