"The terrorists thought that they would change my aims and stop my ambitions, but nothing changed in life, except this: weakness, fear and hopelessness died. Strength, courage and fervour was born," she said in a speech given several standing ovations.
The passionate advocate for girls education was shot in the head by a Taliban gunman as she road on a school bus near her home in Pakistan's Swat Valley on October 12 last year.
She was given life-saving treatment in Britain where she now lives, but the attack has given new life to her campaign for greater educational opportunities for girls.
Gordon Brown, the former British prime minister and UN special envoy for education, hailed Malala as "the bravest girl in the world" as he presented her at the UN Youth Assembly.