The Arsenal and France legend will replace Leonardo Jardim who was given the boot earlier this week.
Monaco are languishing in 18th spot in Ligue 1 after a torrid start to the new campaign.
“Monaco have ended their collaboration with Leonardo Jardim,” the club said in a statement.
“The entire club wish Leonardo and his coaching staff all the best for the next stage of their careers.”
Henry was involved in the Belgium national team’s coaching set-up.
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However, this is his first foray into management.
Having put pen to paper, Henry said: “In the first place, I thank AS Monaco for giving me the opportunity to coach the team of this club so special to me.
“I am very happy to come back to AS Monaco and extremely determined to meet the challenges ahead.
“I can not wait to meet the players to start working together.”
Henry will be assisted by Patrick Kwame Ampadu who was previously Arsenal’s U18 coach.
Monaco Vice President Vadim Vasilyev explained that Henry’s ‘passion’ made him an ideal candidate for the role.
“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.
“He can count on our trust and all our support to bring a new dynamic to the team and carry out its mission. “
Belgium boss Roberto Martinez backed Henry to flourish as the main man at Monaco earlier this week – although he way coy when quizzed about his departure.
“Thierry Henry’s leaving,” he said. “You must be better informed than me.”
“I can’t confirm this news but we all know he will leave us one day,” Martinez said.
“Whether it’s Saturday, a week or six months away, we are prepared for it.
“Thierry has brought all his experience and when he leaves, he will have all our support.
“Thierry has the potential to become a great coach, which he will certainly quickly become.”
Henry had been linked with a move to Aston Villa following Steve Bruce’s departure.
The Championship heavyweights opted to snap up Dean Smith after Henry snubbed the move.