Queiroz stood down after nearly eight years at the helm following his team's 3-0 loss to Japan in the semi-finals of the Asian Cup in January.
The Portuguese, now in charge of Colombia, led Team Melli to qualification for the 2014 and 2018 World Cup finals but they were knocked out in the group stage at both tournaments.
Iran's qualifying campaign for the 2022 World Cup begins in September.
A former international midfielder, Wilmots led Belgium to the 2014 World Cup finals but was sacked after a quarter-final exit at Euro 2016.
His spell in charge of Ivory Coast lasted only six months before he was fired when the West African nation failed to qualify for the 2018 World Cup.
(Reporting by Nick Mulvenney, editing by Amlan Chakraborty)
