Cech joined Arsenal from Chelsea in June 2015 on a four-year deal after falling out of favour with Blues boss Jose Mourinho.
“You are aware of certain things when you play against players, but when you play with them you realise they are really important,” Cech told the Daily Star.
“People always speak about Mesut and the way he has great passing ability,”
“He has but when you see him running, it’s not only about his passing. He’s a far more complete player than just his passing.”
The 26-year-old joined Arsenal from Real Madrid for a club record £42.5 million back in 2013.
Arsenal take on London rivals Chelsea in the Premier League next weekend. Özil is expected to start against the reigning champions and was also part of the Gunners side that beat the Blues in the Community Shield last month.