The Colombian forward raised eyebrows throughout football when he joined the wealthy French side earlier this summer.
However, Falcao has claimed that he is looking forward to getting his hands on silverware following his €60m (£51m) switch from Atletico Madrid.
"Many people may believe that this is a mistake, but I'm sure they will not think that once we have won titles," Falcao told reporters.
"For us the goal is very clear, it is to win all the competitions. Coming to an institution like Monaco is the wish of every player.
"Personally, to know that you are an essential part in a project gives a lot of confidence and serenity. The belief that I could win the important things in this project is the reason that convinced me to come here."