Liverpool were keen on a deal for the Germany striker, and he'd even admitted he wanted to play under Klopp.
"He has scored a lot of goals and has got great experience in the Champions League and obviously with the German squad at international level, so this is a big addition for our club.
"He can raise our level. He's an amazing player. We need to help him find the best position to score goals and to adapt to the league as quickly as possible.
"Hopefully we can be competing for the top next season."