The two South American forwards saw the London club opt against retaining their services beyond their loan deals from Monaco and Corinthians respectively.
Falcao, who arrived at Stamford Bridge exactly a year ago, endured a season disrupted by injury as he managed just two starts and one goal.
Pato joined midway through the season and fitness struggles reduced him to just one start and one sub appearances, bagging a solitary goal in his Blues debut against Aston Villa in April.
Amelia, who was signed on a short-term deal in October last year as cover for the injured Thibaut Courtois, leaves without making a first team appearance.