The striker faced his new club when playing for Atletico Madrid in the Champions League semi-finals, with the Blues captain "surprised" by his opposition's talent in attack
Costa completed his move from Atletico Madrid on Tuesday, two weeks after a deal was agreed to bring the 25-year-old to the Premier League.
The Brazil-born forward played against Chelsea last term, scoring in the second leg of a Champions League semi-final as Atleti triumphed 3-1 on aggregate.
And Costa's efforts over the two legs were enough to convince Terry that he has what it takes to make an impact in the Premier League.
"First of all, his movement and his strength are really good – I was really surprised by it," Terry told Chelsea's official website.
"I think everyone remembers the square-up we had in the first 10 minutes of the first leg of our semi-final game against Atletico Madrid last season, after which I thought, 'fair play'.
"He holds the ball up very well, he has got great movement and he is really physical, but he is very clever with his strength and the way he uses his body. I think he could be a very good signing for us."