The £43million transfer deadline day deal for the Germany international was met with disbelief from several former team-mates at the Bernabeu, with Ozil suggesting he felt no longer central to the plans of Real Madrid manager Carlo Ancelotti following the world-record signing of Gareth Bale from Tottenham.
However, Real Madrid president Florentino Perez has subsequently claimed Ozil in fact asked to leave the Spanish club because "he couldn't handle the pressure at Madrid".
Wenger insists Ozil - set to play at his new home for the first time against Stoke on Sunday - should have no reason to defend himself and can soon take his game to another level.
"I think he is not at the top physically yet, overall we are very pleased to have him with us, but he will demand a bit of time to adjust to the vigorous body challenges he will face here in the Premier league. Once he has done that, he will be even stronger," said Wenger, who had tracked the Germany international since his time at Werder Bremen.
"Real Madrid made a choice they had to let one player go. In the end it was Ozil, but I think he chose us for many reasons.
"One of them was he had the choice to come here before he went to Real Madrid (in 2010), and I had a contact with him from that moment, so maybe it was fate. It was between Madrid and us (then), and this time it was us."
Wenger continued: "I know him (Perez) well and I am surprised by this statement. Honestly, I didn't read what Florentino said.
"I spoke to Ozil about it and he was surprised as well. He said he is not sure that Perez said that completely."
Landing Ozil in what was a club-record transfer saw Wenger finally land the major signing he had craved, having seen bids for both Gonzalo Higuain and Luis Suarez fail earlier during the summer, when France under-21 forward Yaya Sanogo arrived on a free transfer from Auxerre.