The Team Sky general manager ended months of speculation by giving his formal backing to Kenyan-born Froome ahead of the Tour, which starts in Corsica on June 29.
"As always, the team selection is a management decision and it will be evidence-based," Brailsford told Team Sky's official website. "However, it is crucial there is clarity of purpose and, for that reason, we will go to the Tour with one leader.
"Taking that into consideration and given Chris's step up in performances this year, our plan, as it has been since January, is to have him lead the Tour de France team.
"With over seven weeks until the Tour and the Giro [d'Italia] to focus on, our final selection of nine won't be confirmed until after the [Criterium du] Dauphine.
"Everyone here is 100 per cent focused on this race [the Giro] and the next three weeks."
Froome, 27, has been in promising form this season, winning the Tour of Oman, the Criterium International and the Tour de Romandie, as well as finishing runner-up in Tirreno-Adriatico.
Defending Tour champion Wiggins is currently spearheading Team Sky's Giro d'Italia campaign. The 33-year-old's quest to become the first Briton to win the Giro has got off to a promising start following Sky's victory in Sunday's team time trial on the island of Ischia, during which Wiggins took time off his main rival Vincenzo Nibali of Astana.
Prior to the Corsa Rosa, Wiggins spoke of his desire to win both the Giro and Tour, claiming both he and Froome would enjoy joint leadership during the Grande Boucle.
The comment enraged Froome, who took to his personal website to stress that he had been promised team leadership by the powers that be at Sky.
Froome finished runner-up in the 2012 Tour after supporting Wiggins - the designated team leader - during the key mountain stages. With more climbing and less time trials featuring on the 2013 Tour route, the course is said to favour the in-form Froome more than Olympic time trial champion Wiggins.
Brailsford stressed that despite all the media attention regarding his team's leadership, Sky were focused and strong ahead of the season's main targets.
"We are in a fantastic position," he added. "We have two of the best GC [general classification] riders in the world and they are both great racers with a competitive will to win.
"Since the start of season, Bradley's performance plan has focused around training specifically to try and win the Giro and then ride the Tour, while Chris's has been focused on attempting to win the Tour.
"Now we are here. The Giro has started and Bradley has done a brilliant job of getting in the best-possible condition for his assault on the race."