The 25-year-old Costa impressed for Atletico Madrid last season as they won the title in Spain and has now joined Chelsea after they met the £32m buy-out clause in his contract.
And Mourinho told Sky Sports: “He’s a great addition for us. He is a fantastic player.
“Technically he is very, very good. That’s why, lots of the players, they are so happy and so surprised, because his quality is even higher than what they expect.
“He is so strong physically and he gives so much effort during matches.
“When somebody sees him play, the first thing that gets into their eyes is exactly that, the capacity to work hard for the team, and to be so powerful and so strong physically.
“To have Diego, (Fernando) Torres and (Didier) Drogba as our strike force is something that gives us different qualities. We are really strong in that position now.”
Chelsea great Drogba is back at the club after two seasons away and, although he is 36 now, Mourinho says the striker still has the attributes needed to be a success in the Premier League.
“The killer instinct is there, the technique to score goals is still there,” said the Chelsea manager.
“He is still very strong physically. Mentally, exactly the same.
“Every training exercise, every competitive situation in training, his desire to compete and to win is always there. I think he’s an important player for us.”
Chelsea have also signed Cesc Fabregas from Barcelona and Mourinho thinks the former Arsenal man is the complete midfielder.
“I see him as somebody who thinks football faster than the majority of the players,” he said.
“He is the kind of player we need in our midfield to bring us to a different dimension.
“The ball possession, the speed of the circulation, the decisive pass. He has everything.”
Chelsea’s final new boy is left-back Filipe Luis, a team-mate of Costa’s at Atletico last season.
Asked if there were concerns about Luis adapting to the Premier League, Mourinho said: “I don’t think so.
“He is experienced. Very stable, very reliable. He is a player who normally does not make mistakes. He is very stable from a defensive point of view.
“He is left-footed and likes to attack. We need that also, especially against teams who close a lot. We need that kind of creativity.
“We went for stability with these three guys. Diego, Cesc and Filipe. We went for stability and for players who would find it easy to adapt to our team.”