Ozil ended a three-year spell with Real Madrid to join the Gunners last week, with manager Arsene Wenger nearly trebling the club's transfer record to complete a £42.5m move.
Fabregas told The Mirror: "He's going to enjoy the Premier League a lot. It's a league with a lot of space and he is a player who can kill you when he has space.
He has a brilliant final pass and I think the Premier League is going to enjoy him very much. I think he will nail it at Arsenal."
The 24-year-old is due to join his new teammates in North London on Thursday following international duty with Germany in the Faroe Islands.