Deschamps left his 14-year tenure as France manager at the end of the World Cup, with his side losing 2-0 to eventual champions Spain in the semi-finals. They finished fourth after a 6-4 defeat by England in the third-place play-off.
Former Real Madrid manager Zinedine Zidane has been confirmed as the head coach of the France national team.
"I praise Deschamps' efforts, and this is an opportunity to say well done to him. Something new will begin, but the goal is always the same: to win. I will do my utmost for this team. I am eagerly looking forward to joining it. It is immense joy. I am happy with what is happening to me. I cannot find any other words. I am reining in my emotions because I feel so many things inside me. I am ready for the challenge. Winning in 1998 is the best thing that happened to me in my life, winning with my friends. I spent those four or five years waiting for this day. I am deeply moved; it may not show on me, but I am extremely happy."