Terry was appearing on Sky One's A League of Their Own on Thursday night when he was asked what it's like playing with the Atletico Madrid striker.
"Costa has that perception of being arrogant but he's one of the nicest guys I've met in football," Terry said.
"Honestly, off the field he's the nicest guy. On the field he's an absolute animal.
"In training he'd elbow you and look at you and be like 'what have I done wrong there?'
"Off the field I have to say he's one of the nicest guys I've met."