Costa and Falcao played together for Atletico Madrid, with the Colombia international often playing in front, although that role could well be swapped this season.
Falcao managed only four goals in a season on loan with Manchester United and Spain striker Costa feels that poor run of form could prove to be of benefit to the Blues as they look to defend their Premier League title.
“I’ve spent a couple of seasons with Falcao and I reckon things went fairly well,” Costa said. “He did a lot for me and he’s a great striker.
“He’s a top bloke too. He gets on very well with his team-mates and he will help us a lot off the field, in the dressing room.
“He is a really big-hearted guy and that’s the most important thing.
“I think it’s good for us that he didn’t have the best of seasons as that’s why he’s now with us. Radamel knows the sort of manager Mourinho is. He’s a manager who is liked by players because he trusts and backs them. He doesn’t sign a player just for the sake of it.”