Leeds manager Thomas Christiansen had already brought in Pawel Cibicki from Malmo earlier today.
And the boss has been granted a 16th summer signing in Lasogga.
He said: “I want to give all for this club and enjoy my football. I hope we can have a very good season.
“I had to wait for the situation in Hamburg.
“It was not so easy for me but I had to wait. I don’t know which way I could have gone.
“It was the time that I had to change something and Leeds is the right decision for me now.
“I am the typical No 9. My game is in the box.
“I want to help the team with scoring goals and giving assists to fight for the whole club and the team.
“I am a real No 9.”
Leeds confirmed the 25-year-old has signed a season-long loan deal from Hamburg SV.
Leeds United announce signing of Lasogga on loan from Hamburg
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Leeds have acted fast in the past week to replace Chris Wood, who completed his £15million move to Burnley.
Lasogga started his career at Bayer Leverkusen before moving to Hertha Berlin in 2010.
He signed for Hamburg in 2014 after a successful loan spell but last season scored just twice for the club.