Wilcox has worked at City since 2012, initially in several coaching roles before taking on the role of their Academy Director in 2017.
At Southampton, he will be responsible for all football departments, including the men's first team, academy and the women's and girls' programme, the club said.
"Another part of his remit will be player recruitment, an area that will be temporarily overseen by Club Director Rasmus Ankersen until Jason's arrival," the south-coast club said.
“At City he has helped develop some fantastic young players and delivered a pathway for them to be able to comfortably adapt into a competitive first team environment," added chairman Henrik Kraft.
“We are convinced that Jason will continue the great work he has achieved at Man City here at Southampton and look forward to him joining us in the summer.”
A former Premier League winner with Blackburn in 1995, Wilcox will join Southampton in the summer once he has served his notice period with City.
Southampton are bottom of the league on 15 points after 19 games, one point adrift of the safety zone.
They host Aston Villa on Saturday, a game you can follow with Flashscore.
