The Chilean was recently appointed at Manchester City following the sacking of Roberto Mancini.
Cazorla, who worked with Pellegrini at both Villarreal and Malaga, is confident that his former coach will be a success in England.
"He's done spectacular things with Malaga and Villarreal in the Champions League," the Spanish international told Arsenal's official website. "Clubs like City obviously want him for a reason and, ultimately, it's for the job he's done.
"He's had those teams playing spectacular football and I'm sure City will be a better team. I'm sure City's football will change and will be more offensive.
"I'm very happy for him because he deserves to be at a club of that level. He's getting his reward. He's been so important to my career."
Pellegrini has signed a three-year contract with City.