The Atletico Madrid star praised the Scot for his "amazing career" after he announced he would leave his position as Manchester United coach this summer
The Scot is set to stand down after 26 years in charge at Old Trafford, having forged an unparalleled legacy which includes 13 Premier League titles and two Champions League crowns among the 38 trophies he has helped his side win.
Falcao, who remains linked with a move away from the Vicente Calderon this summer, congratulated the managerial stalwart on his success over the years.
The Colombian forward wrote on Twitter: "Stand up, put your hands together and give him a big round of applause! Sir Alex Ferguson is retiring. Congrats for an amazing career!"
David Moyes is set to leave Everton at the end of the 2012-13 campaign and step into his compatriot's shoes at United, Goal revealed following the official confirmation of Ferguson's retirement.
Falcao, on the other hand, is believed to be heading in the same direction as Real Madrid coach Jose Mourinho - from La Liga to Chelsea.