Ronaldo ended his eight-year stay in the Spanish capital after completing a move to the Serie A champions last month.
Costa feels Ronaldo's arrival will take the Old Lady to new heights in the upcoming campaign.
"I think Ronaldo was already at a high level, but he really wanted to take another step to enhance his status," Costa told Italian Football TV.
"I think CR7 has everything to take us to the next level and do important things this season.
"Ronaldo is a really important player, but we also have Dybala and other important players. I've played with Neymar, so it's not totally new for me to play with someone at [Ronaldo's] level.
"Everyone has welcomed him and we know how much he can improve us. We can't hide it, it's clear."
Discussing his career at Juve under head coach Massimiliano Allegri, Costa – who joined the Italian champions permanently from Bayern Munich in the off-season – added: "I think Juventus know how to win a player over.
"Once a player makes a decision and the deal is closed, the club treat them as a member of the family. I think the Juventus family are most important. It's a world where I've learned to live.
"Allegri's a coach with a great passion for the defensive side of the game and, for me, it was really important because I'm a player used to going forward a lot and, working on the defensive side, it's made me a more complete player. He's played an important role in my career."