Tedesco has signed a contract with the Red Devils until after the 2024 European Championships due to be held in Germany.
The 37-year-old has been tasked with qualifying Belgium to the tournament.
Tedesco comes in as a replacement for Roberto Martinez, who left his role after Belgium suffered an embarrassing group stage exit at the Qatar 2022 FIFA World Cup.
Domenico had been without a club after being sacked by RB Leipzig in September last year.
A statement on the official Belgian football website read: "The Royal Belgian Football Association (RBFA) is proud to announce that Domenico Tedesco has been appointed as the new national team coach.
"A Taskforce was formed within the RBFA at the beginning of December, consisting of RBFA CEO Peter Bossaert and Operational Director Football Jelle Schelstraete, RBFA directors Sven Jacques and Pierre Locht, and Club Brugge president Bart Verhaeghe.
"This Taskforce was tasked with finding a new national coach, as well as advising on the further development of RBFA's technical core.
"He [Tedesco] is known as a modern coach with top-level international experience, who likes to play an offensive style of football with plenty of forward pressure. His mission is to qualify the Belgian Red Devils for the EURO 2024 in Germany."
"For me, it is a great honour to be the new head coach of Belgium," Tedesco told reporters following his appointment.
"I'm really looking forward to the task and I'm extremely motivated.
"I had a very good feeling right from the first conversation."
