Sources told ESPN FC on Friday that the 41-year-old would sign a three-year contract, and he has now committed to take charge of the club where he began his professional playing career until 2021.
Monaco is now 18th in Ligue 1 with just one win from their opening nine games.
This is Henry's first foray into management and he will soon leave from the role of second assistant coach of the Belgium national team under Roberto Martinez.
Jardim led the club to Ligue 1 glory in the 2016-17 campaign, ending Paris Saint-Germain's stranglehold on the title, and reached the semi-finals of the Champions League in the same season.
He started his career at Monaco in 1994 under former Arsenal boss Arsene Wenger, before joining Juventus in 1999.
Patrick Kwame Ampadu, a coach at Arsenal's academy and father of Chelsea and Wales player Ethan Ampadu, will join Henry's coaching staff, alongside Benfica Under-23 coach Joao Carlos Valado Tralhao.
Henry knows Monaco well having graduated through the youth system and played for the Principality club between 1993-99.
In a club statement, Henry said: 'In the first place, I thank AS Monaco for giving me the opportunity to coach the team of this club which is so special to me. "I can not wait to meet the players to start working together", said Thierry Henry.
Vadim Vasilyev, Monaco vice president and CEO added: "His knowledge of football, his passion for the game, his high standards and his commitment to our colours make his nomination a reality".