Chelsea have officially confirmed that Falcao, Alexandre Pato and Marco Amelia have been released by the club.
The Italian goalkeeper has never made his official debut for the club after joining in October 2015 to be Asmir Begovic's backup.
The Colombian was a gamble by then-manager Jose Mourinho who joined the club on a season-long loan deal with the option of a permanent transfer at the end of the season.
He only made 10 appearances in all competitions as his struggle with injuries continued.
The 30-year-old will return to Monaco.
Pato moved to London on loan from Corinthians during last January's transfer window, scoring a penalty on his debut in a 4-0 victory at Aston Villa in April.