Renard will be presented at the Stade Bonal on Friday after opting to quit his post as Zambia boss and succeed Eric Hely at the Ligue 1 strugglers.
The 45-year-old took over the Zambia role for a second time in October 2011 and led them to their greatest triumph when they won the African Nations Cup four months later.
The Football Association of Zambia (FAZ) announced his departure on Monday morning with Sochaux swiftly confirming he would be taking over the Montbeliard club.
FAZ spokesman Eric Mwanza said in the statement: "FAZ and Herve have consulted and it has been agreed not to stand in his way.
"It is a compliment for a coach working in Africa to be head-hunted by a top European club.
"It makes us proud to be able to take ownership of Herve's rise as a successful international coach.
"FAZ wishes to thank Renard for his dedication to duty, hard work, proficiency and wish him well as he takes up his new coaching job.
"Following the departure of Renard, assistant coach Patrice Beaumelle will take charge of the Chipolopolo starting with the international assignment against Brazil in Beijing next week Tuesday 15th October 2013."
Renard will need to hit the ground running with his new club, who are second from bottom having won just one league game all season.
Hely stood down in the aftermath of Sochaux's 5-1 thrashing at promoted Guingamp on September 25.