The Colombia international stunned the footballing world by completing a €60 million (£50m) move to Stade Louis II from Atletico Madrid earlier this summer, having previously been tipped to join one of Europe's superpowers.
But he remains insistent that he has made the correct career choice and believes people will be eating their words once the club begin to win trophies.
|3/1||Falcao is 3/1 with Paddy Power to be Ligue 1 top scorer this season
"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.
"Many people may believe that this is a mistake, but I'm sure they will not think that once we have won titles."
Falcao, who is widely considered one of the world's best strikers, scored 52 goals in just 62 appearances for Atleti and hopes he can continue his goalscoring exploits in France.
"As I have always said, my goal is to score as many goals as it will take to crown ASM the Ligue 1 champion. If I score a lot, I'll be happy."
The former Porto star then welcomed the club's newest additions, former Barcelona defender Eric Abidal and ex-Malaga midfielder Jeremy Toulalan, who Falcao believes will have a positive impact on the newly-formed squad.
"I am very happy to play with Abidal and Toulalan. I had the opportunity to play with them, they are excellent players who are experienced, they will enhance the potential of the team."
Ricardo Carvalho - who joined after leaving Real Madrid - and Porto pair James Rodriguez and Joao Moutinho are Monaco's three other big name signings so far this summer.