The award to Deschamps was in recognition of his work in leading the French side to glory at the 2018 World Cup in Russia.
The 49-year-old won ahead of Zlatko Dalic who guided Croatia to their first every World Cup final in Russia and Zinedine Zidane under who Real Madrid won a third consecutive Champions League title.
France’s World Cup triumph in Russia meant Deschamps became just the third man to win the World Cup both as a player and a coach.
In the Best Player category, Croatia’s World Cup captain and Real Madrid midfielder Modric ended Cristiano Ronaldo and Lionel Messi’s decade-long domination of the award.
Modric beat Liverpool’s Egyptian forward Mohamed Salah and Ronaldo.
“The emotion is huge because it is thanks to the work of everyone. So many people have come together and so many have supported me,” Modric said.
Salah won the Puskas award for best goal for his strike against Everton last December.
For the first time in 12 years, Messi was not among the finalists.
Thibaut Courtois won the best goalkeeper award while Brazil’s Marta was crowned best women’s player for a record sixth time. Lyon’s Reynald Pedros won the award for best women’s coach.