The Colombia international returned to Stade Louis II a year ago looking to get his career back on track after two injury-ravaged seasons in the Premier League.
Successive loan spells at Manchester United and Chelsea yielded just five goals in 41 appearances combined, but Falcao rediscovered his form in France, scoring 21 goals in 29 league outings to help Leonardo Jardim's side clinch the title.
The 31-year-old striker formed a lethal partnership with rising French star Kylian Mbappe as the principality outfit reached the Champions League semi-finals before being knocked out by Juventus.
Upon signing his new deal, the club captain said in statement: "I am happy to continue my adventure at AS Monaco. 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."