After Goal exclusively broke the story on Sunday, the former Real Madrid star sealed a £40 million switch to the Premier League on transfer deadline day to become Arsene Wenger's fourth and final addition of the window.
A number of Madrid players have expressed their surprise and disappointment at Ozil's departure and Podolski is looking forward to playing with his international colleague when he recovers from a hamstring injury.
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"It's great that he's coming - he's a good friend and a brilliant footballer.
"He's a great fit for us. We're already playing great football; the only thing that was missing was the final punch, that element of surprise. That's exactly what Mesut will give us.
"It is extremely sad, I would have liked to have played with Mesut straight away, not watched him from the stands, but I can't change that. I can't sew the muscle back together again."
Ozil's first opportunity to play for Arsenal is set to come when they face Sunderland on September 14, following his international duty that sees Germany come up against Austria and the Faroe Islands in World Cup qualifying.