The 25-year-old played a major in helping Mumbai win the ISL title, contributing with three goals and seven assists.
Prior to signing for the Islanders, Boumous spent three seasons with FC Goa and made the switch to Mumbai last season for a record transfer fee.
The Frenchman has provided the highest numbers of assists in the history of the competition (24 in 56 games), and won the Golden Ball award while playing for the Gaurs during the 2019-20 season.
"I know Kolkata as the Mecca of Indian football," Boumous said.
"I am happy to sign with the city's traditional and successful club, ATK Mohun Bagan. I have heard that the joy of playing in front of millions of supporters of the Green-Maroon team in Yuba Bharati is different and I shall play this time to win them.
"I am always hungry to win the trophy. I have brought success to the clubs that I have played in. And I shall keep this in mind as I play again. I will do my best to win. I am looking forward to seeing the passion and excitement of the Green Maroon supporters after winning the match. Sanjiv Goenka, the principal owner of the team, inspired me to come to Kolkata. I am grateful to him. My goal is to win the AFC Cup and the Indian Super League.
“Both scoring goals and helping to score goals are equally rewarding. I get pleasure from both. The team’s victory is the main purpose. That is not possible without goals."
Hailing his new signing, coach Antonio Habas added: "Hugo is a very fast and technically successful footballer. His personal skills are also very good. Hugo can create attacks as well as counterattacks. That is why he is so successful. With the arrival of Hugo, the strength of the team increased a lot."