The German international, who joined up with his new teammates following Euro 2012, signed for the Gunners from Cologne in April.
"I am now two weeks into training and it is not easy when you come back to your club after a European Championship or World Cup," the 26-year-old told the club's official website.
"I need some more weeks and then you will see the real Podolski.
"It has been very good so far. This is a big club with a great coach and I am very proud to be an Arsenal player. I am looking forward to the first match of the season against Sunderland."
Arsenal face Podolski's former club Cologne in a pre-season friendly in Germany on Sunday.