The Colombian forward was the subject of interest throughout last season from major clubs including Manchester United, Chelsea, Real Madrid and Paris St Germain, but in the end opted for the Ligue 1 outfit from the Mediterranean Principality, owned by Russian billionaire Dmitry Rybolovlev.
The move was made official on May 31, after Monaco paid Atletico Madrid an estimated 60million euros and agreed a five-year contract with the player. And in his first press conference as a Monaco player on Tuesday, Falcao said: "Many people think that coming here may be an error and perhaps they are right. But when we win a trophy, I'll know it was the right decision."
He added: "Choosing a club that isn't in Europe may have surprised some people but we want to be in the Champions League next season. That's our motivation."
Falcao explained he had moved to the Ligue 1 side "for a number of reasons".
"The president and his coaching staff have the same ambition as me, which is to reach the top of European football," he said.
"They assured me that I was as a fundamental part of this project, which gave me confidence and security. This club wants to win trophies and that, together with the role I'll have in the team, made me want to come here."
Falcao will play a leading part in a squad that includes compatriot James Rodriguez, plus Portuguese players Joao Moutinho and Ricardo Carvalho. The club announced the signing of Eric Abidal on Monday while Jeremy Toulalan joined last weekend.