The 41-year-old French World Cup winner, who had been working as an assistant to Belgium coach Roberto Martinez since 2016, returns to the club where he began his professional career.
Henry, who has signed a contract with Monaco until June 2021, said it was "fate" that he had returned to the Principality.
Henry replaces Leonardo Jardim, who in 2017 guided Monaco to their first Ligue 1 title since 2000. He was sacked on Thursday after a string of poor results left Monaco in the relegation places.
The former striker will be joined by Joao Carlos Valado Tralhao, under-23 coach at Benfica, and Patrick Kwame Ampadu, coach at Arsenal's academy and father of Chelsea player Ethan Ampadu.
Henry graduated from Monaco's youth system and made his debut for the club in 1994.
He notably scored seven goals in the 1997-8 Champions League as the Monaco team of the time, then coached by Arsene Wenger, reached the semi-finals, where they lost to Juventus.
"It is with great pride that I am delighted to announce that I have accepted the position to become the manager of AS Monaco FC," he said on Twitter.
"I was fortunate to receive some very attractive offers over the last few months but Monaco will always be close to my heart.
"Having started my footballing career with this great club, it seems like fate that I will now begin my managerial career here too.
"I'm incredibly excited to be given this opportunity but now the hard work must begin. Can't wait."
After spending five seasons as a player with Monaco, Henry went on to play for Juventus, Arsenal, Barcelona and the New York Red Bulls.
While at Arsenal, he was the Premier League's top scorer for four seasons and won two league titles. He has been tipped as a future manager of the London club.
"A big opportunity with @AS_Monaco, a club close to your heart -- and we'll be rooting for you," a tweet from Arsenal said.
Henry scored 51 goals in 123 appearances for France, winning not only the 1998 World Cup but also Euro 2000.
After the duo oversaw Belgium's 2-1 win against Switzerland in the Nations League on Friday, Martinez said Henry "has the potential to become a great coach".
Henry's first game in charge will be against Strasbourg in the league on October 20 with a must-win Champions League tie against Club Brugge four days later.
Monaco chief executive officer Vadim Vasilyev said Henry could "count on our trust and all our support to bring a new dynamic to the team and carry out the mission".
"His knowledge of football, his passion for the game, his high standards and his commitment to our colours make his nomination a reality.
"Thierry is both aware of the task ahead and eager to start his new job."