Ozil joined the Gunners from Real Madrid last Monday just hours before the transfer window closed, ending manager Arsene Wenger's summer-long search for a marquee signing.
Mertesacker told the Daily Mail: "I think he is worth what we paid for him. He is a phenomenal player and I think he has not reached his best, at the moment.
"He will fit in. He will suit Arsenal. I think his contribution to this club will be massive. He's an exceptional player and we are over the moon to have him at Arsenal.
"He's shy but he developed in the last few years. When he went to Madrid, went abroad, I think he improved a lot. He went through rough times as well so his experience is vital and can make the difference."
Mertesacker and Ozil will both be in action for Germany against the Faroe Islands this evening before returning to Arsenal ahead of a trip to Sunderland on Saturday, which could mark the 24-year-old's debut for the Gunners.