Falcao began this season with a bruised reputation after a pair of chastening Premier League seasons on loan at Manchester United and Chelsea, but he has been back to his sharp-shooting best with 21 goals in 29 league games helping Monaco to their first top-flight title since 2000.
"I am happy to continue my adventure at AS Monaco," the club captain said in a statement.
"After this incredible season where I found all my motivation, I had only one desire: to prolong this beautiful story!
"I am confident that this project will be just as exciting next season with the desire to aim for the best."
Taking on a role as more of an elder statesman in Leonardo Jardim's exciting team, Falcao has been paired with emerging France star Kylian Mbappe this season.
Mbappe has spoken highly of their burgeoning partnership, saying: "I think I'm the luckiest player in our squad, because I'm at the start of my career and get to play alongside a top striker like Radamel. He's made his mark on the history of the game and scored a huge number of goals."
Tying Mbappe to renewed terms may be Monaco's next priority in the face of reported interest from Real Madrid and Manchester United.
News of Falcao's deal comes in a busy close-season for Monaco after they sold Bernardo Silva to Manchester City in a reported €50million deal.