Mourinho was always going to add another striker to his ranks after the departure of Didier Drogba but some may have been surprised by the arrival of Falcao - who only scored four goals for United during his loan spell from Monaco last season.
He told ESPN: "When he went to Man United I have to say I was a bit scared. Because he's a predator in the box and a guy who does score goals all the time. He did that in every club in every league, so I was convinced he was going to do that in our league, in England.
"We had a very exhaustive analysis of his condition before we made a decision. Our doctor had real work to investigate all of that. He is not, for sure, a physical problem. So if it's not physical, we can make him score goals again."
Diego Costa is likely to be the main forward at Stamford Bridge going into the start of the season after an impressive debut season at the club, but he has shown he is vulnerable to injuries, meaning there is a need for an adequate replacement.
Prior to his arrival in the Premier League, Falcao had a reputation of being something of a goal machine given his record at both Porto and Atletico Madrid - but had been recovering from a serious knee injury picked up during his first season at Monaco.
Last season was obviously a disappointment for the Colombian as he failed to live up to that billing but Mourinho clearly feels the forward has something to offer Chelsea, and thinks he can get the best out of him. The odd occasion to potentially play with Costa who was a former strike partner during their time together at Atletico could also help Falcao rediscover his best form.
It will be interesting to see how Falcao gets on in the season ahead, as he is likely to have more game time than he did at United, purely because of the European fixtures Chelsea have to contend with.