The Ligue 2 champions have already secured the services of a number of high-profile names with Falcao, James Rodriguez, Joao Moutinho and Ricardo Carvaldo, and the Colombia international is keen to challenge for major trophies.
"I am very pleased with the confidence Monaco have shown in me by signing me. Monaco have a very interesting sporting project going on. We all want to help Monaco to the top of Europe," the striker, 27, was quoted as saying by AFP.
"The conditions here are Monaco are very well, not just football wise, but also when it comes to other personnel. Rodriguez is a great player. That's why Monaco paid a lot of money for him."
Falcao is currently away on international duty with Colombia as it takes on Argentina on June 7, followed by Peru four days later, as it looks to boost its chances of World Cup 2014 qualification.