Voldemort was killed by his own rebounding "Avada Kedavra": curse. Voldemort was wielding the Elder wand during his and Harrys duel.
The previous master of the wand was Draco Malfoy. But when Harry captured Draco's wand from him--the Elder Wand also became his.
Since Harry was rightfully the owner of the wand, it refused to kill Harry. So the killing curse rebounded against Harry's "Expelliarmus" spell and killed Voldemort.