The Frenchman joined Les Rouge et Blanc from Sevilla last week for £17m, having been linked with a whole host of European clubs.
Kondogbia is confident that he can learn from the more experienced players at the Stade Louis II and is looking forward to beginning his new adventure.
"I am really proud to begin this project with AS Monaco and I hope to achieve all the objectives that the club have asked of me," Kondogbia said in a press conference.
"Personally, in my position, I know that I can learn a lot from working alongside someone like Jeremy Toulalan and from somebody like Eric Abidal in terms of experience. It is great to be able to play with players like them and I think that will help me make great strides in terms of my career.
"It is a new step, a different project to what I have been involved in before. I'm really pleased to have signed here and can't wait to help out Eric Abidal, Falcao and all the other players.
"I think with the squad the club has, the aim has to be to get into the Champions League. Personally, my aim has always been to play as much as possible and as well as possible and that remains the case."
Kondogbia is currently on international duty with France.