Chelsea boss Jose Mourinho says striker Falcao was signed to take over from Didier Drogba in his squad's offensive department.
The Colombian spent last season at Manchester United but Louis van Gaal opted against extending his stay at Old Trafford.
But Mourinho says Falcao is still one of the best in the business and will bring experience and goals this season.
"When a player is injured or has bad consequences of a big injury there is sometimes nothing you can do," Mourinho is quoted as saying by Goal.com.
"We made ourselves sure that was not the case with Falcao because if that was the case he would not be with us.
"He didn't perform [at United] for many reasons. Some players don't perform with me, some players don't perform with Chelsea, they go to other clubs and they perform.
"This can happen, so we know that Falcao is in good conditions related to the surgery he had before he went to Man United.
"We believe that he can with us and to replace a big player like Didier we wanted to go with another big player with experience, ready, so these three strikers for us – Falcao, Remy and Diego.
"We are very happy."