The Frenchman was confirmed as Leonardo Jardim's replacement on Saturday morning after days of negotiations with his former club.
The former striker will be joined by Joao Carlos Valado Tralhao, under-23 coach at Benfica, and Patrick Kwame Ampadu, coach at the Arsenal Academy.
Henry knows Monaco well having graduated from their youth system and making his professional debut for the Principality club in 1994.
Henry has previously spoken of his dream to take the managerial reins at the Emirates, but it seemed on that occasion that the club's all-time leading scorer's lack of managerial experience counted against him, as Unai Emery was installed by Ivan Gazidis ahead of Henry and others.
Henry has signed a deal until June 2021 and said on Monaco's website: "I am very happy to come back to Monaco and extremely determined to meet the challenges ahead".
Henry is also his France's leading scorer with 51 goals and won the World Cup in 1998 and European Championship in 2000 with Les Bleus.
Henry was with Belgium on Friday as they beat Switzerland 2-1 in the Nations League.
"I thank AS Monaco for giving me the opportunity to coach the team of this club which is so special to me", he said.
"(Henry's) knowledge of football, his passion for the game, his high standards and his commitment to our colours make his nomination a reality", said Monaco's chief executive Vadim Vasilyev.