The Gunners brought in the German playmaker from Real Madrid for £42.4million on deadline day with Wenger suggesting he was fairly confident of securing his services prior to the Sunday, September 1 North London derby clash with Tottenham.
"When I told you two or three days before (the deadline), I looked a bit lonely when I said I was optimistic but, in the end, it happened," said Wenger.
"I thought we had a chance to do it, a small one, but we worked very hard on it until the end.
"It was very complicated in the end because the timing was short but, on Sunday when I came to the Tottenham game, I thought we will manage to do it. Before the game, I knew we were 90% there.
"What is very important for us is to find world-class players. There are not plenty around.
"We had to go through some years when I signed a long-term contract where we had some restricted financial potential, and the target was to stay in the Champions League in this period.
"We managed to do it, and we are now in a strong position financially."