The transfer was confirmed by all parties yesterday.
Wenger said: "We are delighted to secure the deal for Lukas Podolski and see him as an important part of our future.
"He is a top-class player, a very good finisher and a proven performer at club and international level.
"He is a very strong player and will provide us with good attacking options.
"We are happy to have made this signing early and we're looking forward to watching Lukas contribute at the European Championships over the summer, a level where he has already made 95 caps at the age of 26 - a phenomenal record and just shows his quality as a player."