Thousands of people had signed an online petition appealing for a change of heart over 18-month-old Marius.
The zoo said it had no choice because of European rules to avoid in-breeding.
Marius was due to be killed by a bolt gun, not a lethal injection, which would contaminate the meat.
Two zoos, one in the UK and one in Sweden, had reportedly put in last-ditch offers to take Marius in.
On Saturday Bengt Holst, scientific director at the Danish zoo, defended Marius’s destruction, saying his genes were already well represented among giraffes at the zoo.
He said he could not understand the fuss over Marius, pointing out that, for instance, 700-800 deer are killed every year at a deer park north of Copenhagen to control their numbers.
The zoo planned to dissect the animal after it was killed, before feeding it to the tigers and other carnivores.
“It would be absolutely foolish to throw away a few hundred kilos of meat,” Bengt Holst said according to the Swedish newspaper Svenska Dagbladet.
“Some is used for research and the rest for food.”
Animal rights campaigners have described the move as barbaric and have accused the zoo of being unethical.
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