Mourinho mainly played Costa as a lone striker last season in a 4-2-3-1 system but, following an excellent start, he struggled with injury towards the end of the campaign, though he finished with an impressive 20 goals in 26 Premier League appearances.
Falcao, by contrast, was at Manchester United last season on loan from Monaco but struggled to make an impact, scoring just four goals in 29 games.
For the forthcoming season, he has swapped Old Trafford for Stamford Bridge and his new boss is sure he can get the best out of him.
He said: “I’m very happy with his first week. I like him a lot as a player. The team play very well with a striker of his quality.
“He’s not just a guy that can score a goal; he can also contribute a lot to the quality of the game.”
The Colombian only joined up with his new team-mates on their recent pre-season tour of the United States but played in a 2-2 draw against Barcelona in New York last week alongside Loic Remy.
Mourinho added: “They did very well not just to bring the team forward but also with one less player in midfield they closed the spaces in front of the midfield line. We can play with two.
“Falcao came on and suddenly the team was direct and objective. They closed the lines and played in the opposition half. Falcao held the ball up very well.”