The 48-year-old Wilmots was coach of Belgium between 2012 and 2016 and lead them to the World Cup in Brazil.
He was sacked in July 2016 after Belgium lost 3-1 to Wales in the quarter-finals of the European Championships.
Frenchman Dussuyer quit the Elephants after they exited the 2017 Africa Cup of Nations at the group stage.
Wilmots, who has signed a two-year contract with an option to renew, will get the chance to see his new charges in action almost immediately as Ivory Coast play two friendlies.
However he will not be in charge of the team for those matches, against Russia on Friday in Krasnador and then Senegal three days later in Franceas, as Ibrahim Kamara will be in temporary control.
The Belgian has been set the task of qualifying for the 2018 World Cup in Russia and the Africa Cup of Nations a year later.
Ivory Coast are top of their World Cup qualifying pool with four points from two matches, ahead of Gabon, Morocco and Mali, with only the group winners going to Russia.
When the Nations Cup campaign kicks off in June, the Elephants will battle it out with Guinea, Central African Republic and Rwanda for a place at the finals in Cameroon.