The Chelsea boss hailed the "phenomenal" German, describing the club-record summer signing as key to the Gunners' unexpected run at the Premier League title this season.
The German was a surprise club-record 50 million euro deadline-day signing at the Emirates Stadium, notching four goals and a league-high seven assists since his arrival.
Mourinho worked with Ozil for three years at Real Madrid, and he feels the midfielder - along with the maturing talents of Aaron Ramsey and Theo Walcott - can guide Arsenal to the title.
"Mesut is a phenomenal player, one of these players that you buy to complete the puzzle of your team," Mourinho is quoted as saying by The Guardian. "You don't need time with him, you need nothing. The player just arrives, his quality and his maturity and his leadership. ... You put him in and you know automatically your team becomes better.
"There are many ways to improve your team. One of them is to work with young players and another is to go directly to the market and buy one of these finished products. Arsenal had the chance to do it with Mesut and they did very well. I think, in the deep of their souls, [Arsenal] think they can [win the title]. In my previous time here, Walcott was a kid. He's now a man. Other players are in the best moment of their careers - [Jack] Wilshere, Ramsey and [Kieran] Gibbs."
Mourinho - who missed out on No.1 target Wayne Rooney during the summer - was less positive about Chelsea, hinting that fans will have to wait until next season for the first piece of silverware of the Portuguese's second spell.
"Next season, Chelsea will have a phenomenal team," Mourinho said. "Between the work we are doing [on] the evolution of the players and a couple of clinical signings [next summer]. When you buy two clinical players to complete the puzzle you are building, I think that Chelsea next season will have a really very good team."