Chancellor Angela Merkel and President Joachim Gauck were among 2,100 guests invited to the inaugural evening concert under tight security at the grand hall of the Elbphilharmonie, which has electrified critics with its audacious design and world-class acoustics.
Billed as a cultural monument ready to rival the Sydney Opera House, the building came in more than six years overdue and at 10 times the initial budget, with a cost to the city-state of 789 million euros (USD 829 million).
"It was a difficult birth but they have adopted the child," he said of the 1.7 million residents of Germany's second city who have footed the bill.
Jutting out from the city at the end of a pier on the Elbe River, the Elbphilharmonie has a boxy brick former cocoa warehouse as its base, with a breathtaking glass structure recalling frozen waves perched on top.
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Scholz insisted that the Elphie, as the two-hall concert house has been nicknamed, would be a building for the people, with diverse events appealing to visitors beyond the well-heeled classical music set.
"It is my aim that every pupil in a Hamburg school will see a concert here," he said.
The completion marks a rare urban development success story in Germany, which has been plagued by planning disasters such as Berlin's international airport, now five years behind schedule and counting.
The programme for the opening has been kept secret but is meant to span 400 years of music history, including Beethoven, Wagner and contemporary composer Wolfgang Rihm.
For those not lucky enough to snag tickets, a music-and-light show will be staged in the evening, projected on to the Elbphilharmonie facade.