Wilmes still has to be officially approved by King Philippe, who is expected to announce the appointment at the earliest on Sunday.
Michel will take over the post of EU Permanent Council President on 1 December. He said earlier this week that he expects to leave the prime minister post by early November.
Wilmes will lead an expedition government. Belgium has not had a fully functioning government since the coalition Michel when the coalition collapsed in December 2018.
Wilmes is considered a close ally of Michel and elected to Parliament in 2014.