The Blues have brought in striker Michy Batshuayi from Marseille for £33million and midfielder N'Golo Kante from Leicester City for £30m so far this summer and young defender Zouma expects them to have an immediate impact on Antonio Conte's squad.
I know Michy and he's a very good striker,' the injured 21-year-old told the club's official website.
"He's only 22 and it's great to have another talented player in the team. The manager will have a lot of options, which is a nice problem for him and when there is competition for places everybody improves.
"He doesn't speak English so we are all here to help him settle. A few of us speak French and there is a very good team spirit here, we are all friends.
"Kante will bring a lot to the team. We saw him in the Premier League last season with Leicester and he was unbelievable. He runs all over the pitch, makes lots of tackles and interceptions and he's very effective with and without the ball.
"The midfield area, like the attack, is full of competition and that's really good for the whole team."