The 22-year-old has been linked with a move to St James' Park but has now finalised a deal with Hamburg.
The 22-year-old spent last season on loan with HSV and was expected to make the move permanent this summer.
However, reports had surfaced that the Magpies were interested in bringing the striker to St James' Park. And when Hamburg and Hertha Berlin disagreed on the valuation of the striker, Alan Pardew's side were presented with a little slice of hope.
That interest has now ended, though, with Lasogga joining Hamburg on a permanent deal.
"It's fantastic that this transfer has now been perfected and that my situation has been resolved," the striker said of his move. "I'm delighted that I can continue playing for HSV."
Lasogga joins Bafetimbi Gomis in the list of strikers Newcastle reportedly registered interest in but could not persuade to move to St James' Park.
Their next target appears to be Luuk de Jong, who spent last season on loan at the club, although the Magpies have other targets lined up, including Alexandre Lacazette.
Newcastle have also already brought forward Ayoze Perez to Tyneside, while new £6 million man Siem de Jong (Luuk's brother) can also play up front.
Pardew spoke of the difficulty of recruiting strikers last month and stated that he expected more action after the World Cup and in August. The wait goes on.