The 26-year-old is joining Arsene Wenger's side for an undisclosed fee.
Podolski has scored 18 goals this season in 28 league appearances for the Bundasliga side.
"I'm so happy to be joining Arsenal Football Club and to play in the Premier League. Arsenal is one of the top clubs in Europe with a huge history," Podolski said.
"There are many top quality players at Arsenal and the style of football which the team plays is fantastic."
Manager Arsene Wenger said he was "delighted" to secure the deal: "He is a top-class player, a very good finisher and a proven performer at club and international level.
""We are happy to have made this signing early and we are looking forward to watching Lukas contribute at the European Championship over the summer."
With 95 caps, Podolski has scored 43 goals for Germany since making his international debut in 2004, and was part of the 2010 World Cup squad.
What Do You Think? Nice Move By Wenger?
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