The Belgian FA said he would sign a contract until after Euro 2024 and that his first game in charge will be their opening qualifier against Sweden in Stockholm on March 24th.
Tedesco, who was born in Italy but grew up in Germany, has also coached Schalke 04 and Spartak Moscow.
"For me it is a great honour to be the new head coach of Belgium," Tedesco said in a statement. "I'm really looking forward to the task and I'm extremely motivated. I had a very good feeling right from the first conversation."
Martinez left the role after Belgium crashed out in the first round of the World Cup in Qatar in December. He has since been named Portugal manager.
Belgium's plans to name Tedesco had been hampered by his contract negotiations with Leipzig. He was fired in September but is still entitled to an estimated one million euros ($1.07 million) in wages, sources had told Reuters on Tuesday.
