Stewart will remain in the job until February 15 to ensure a smooth transition before heading to the Netherlands to join PSV Eindhoven.
The federation said it was seeking a new sporting director, who will be charged with hiring the men's team's next head coach after Gregg Berhalter's contract expired at the end of last year.
Anthony Hudson will serve as the men's coach until a permanent head coach is named, and US Soccer said it has hired Sportsology Group to lead the search for the next sporting director.
McBride said he had decided to move on from the role he has occupied for three years prior to last year's World Cup, in which the team reached the round of 16.
It has been embroiled in turmoil since returning from Qatar amid a bitter dispute between Berhalter, US midfielder Gio Reyna and his parents.
After the World Cup Berhalter made remarks criticizing Reyna's commitment to the team and effort at the international tournament, saying that he even considered sending him home.
Reyna's parents, who have known Berhalter and his wife for decades, responded by informing the federation of a dispute between Berhalter and his wife outside a bar 31 years ago that turned violent, prompting an ongoing investigation by US Soccer.
Berhalter has said he regrets kicking his wife of 25 years in the legs during the 1991 dispute and that they ultimately reconciled and learned from the incident.
He has said he hopes to be rehired as the team's head coach and US Soccer president Cindy Parlow Cone has said he is a candidate.
Later on Thursday MLS side Austin FC announced that Gio's father, Claudio Reyna, would step down for his position as sporting director at the club but stay on in an advisory role.
The former US men's national team captain has admitted to sending messages to US Soccer during the World Cup venting his frustration with Gio's limited playing time at the tournament.
Claudio's wife Danielle then informed US Soccer officials about the incident between Gregg and Rosalind Berhalter, ESPN reported.
Berhalter has said that alerting US Soccer to the incident was part of an effort to "take him down".
