Costa joined Chelsea from Atletico in 2014 after spending six years over two spells with the Spanish club.
"Diego Costa is our player, he's a fantastic player with fundamental importance. He's very happy and is working hard," Conte told reporters on Tuesday.
Winger Juan Cuadrado was shipped out on loan to Juventus last season and scored five goals in 40 appearances to help the Italian side to the league and cup double.
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Conte said he was willing to give the Colombia international a chance to prove himself at Stamford Bridge.
"Cuadrado is Chelsea's player. I like him. He arrived today and this afternoon he starts to train with us," said the 46-year-old during the club's pre-season training camp in Austria.
Conte will begin his tenure in England with a London derby against West Ham United at Stamford Bridge on Aug. 15.
(Reporting by Shravanth Vijayakumar in Bengaluru, editing by Pritha Sarkar)
