The 29-year-old Falcao developed a reputation as one the most feared strikers in Europe, netting 72 goals for Porto in two campaigns and 70 goals in two seasons for Atletico Madrid before joining AS Monaco in 2013 for almost $80 million.
However, following an anterior cruciate ligament injury that ruled him out of the 2014 World Cup, Falcao joined Manchester United on loan last season but scored four goals in 29 games.
"Radamel knows the sort of manager Mourinho is: one who is liked by players because he trusts and backs them," Costa told reporters.
"He doesn't sign a player just for the sake of it, it's because he has confidence in him and wants him to feature regularly.
"It's good for us that he didn't have the best of seasons as that's why he's now with us."
Falcao, who has joined Chelsea on a season-long loan from Monaco with an option to make the deal permanent, played alongside Costa at Atletico and the duo tormented Real Madrid in the 2013 King's Cup triumph.
"I spent a couple of seasons with Falcao and things went fairly well," Costa said.
"He did a lot for me and he's a great striker. Whether the manager chooses to play us alongside each other, that's up to him, but he is very talented."
Costa scored 20 goals for Chelsea in his debut season at Stamford Bridge after joining from Atletico for 32 million pounds ($49.63 million).
However, the fiery Brazilian-born Spanish striker had his temperament called into question when he was banned for three matches for a stamp on Liverpool's Emre Can.
"I won't change my style," Costa said. "I haven't done anything malicious.
"I've always played this way for all the sides I've been with and I've scored a lot of goals in this style.
"The key for me is to score goals and win trophies, if I change in any way, I'm not going to be the same player.
"The aim is to win the Champions League. We have a squad here capable of winning it."
($1 = 0.6447 pounds)
(Reporting By Michael Hann; editing by Amlan Chakraborty)
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