Falcao joined the Blues on a year-long loan from Monaco last summer after a miserable spell at Manchester United the season before.
But the Colombian hitman failed to make an impact at Stamford Bridge and poor form and injury restricted the 30-year-old to just 12 appearances in all competitions.
Fellow striker Pato also struggled to impress after joining the Blues on loan from Corinthians in January.
The 26-year-old played just twice for the club, scoring once, and has now been sent back to the Brazilian side.
Goalkeeper Marco Amelia, who arrived on a free transfer in October as cover for injured first-choice goalkeeper Thibaut Courtois, has also left the Premier League side.