The copper-clad building - pictured here in an artist's impression - will hold 7,000 spectators, although capacity will be reduced to 6,000 after the Games.
It will have retractable seating to allow use for several different sports once the Olympics have finished.
All qualifying matches for handball will be held at the arena, though the semi-finals and final will take place at the larger basketball arena.
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"The vibrant Handball Arena will provide a great experience for competitors and spectators during the games," said John Armitt, the Olympic Delivery Authority chairman.
Armitt added that it would also bring a long-term, "sustainable and flexible" facility for local people.
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