The 37-year-old Italian succeeds Roberto Martinez on a deal that runs to after the 2024 European Championship in Germany.
Belgium open their qualifying campaign with an away match against Sweden on March 24.
Tedesco told the Royal Belgian Football Association's official website: "For me it is a great honour to be the new head coach of Belgium.
"I'm really looking forward to the task and I'm extremely motivated. I had a very good feeling right from the first conversation."
Tedesco, who had spells in charge at Spartak Moscow and Schalke, had been out of work since leaving Leipzig in September.
Martinez had a six-and-a-half-year stint as Belgium boss during which he guided them to their best World Cup finish with third in Russia in 2018.
He stepped down in December after the team's shock group-stage exit in Qatar, and has since become head coach of Portugal.