All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
It is permitted to eat meat of animals slaughtered by non-Muslims under the following conditions:
1) The butcher must be a Christian or Jew.
2) He must mention Allah's Name while slaughtering; otherwise, it is forbidden especially in case of mentioning Christ's or Ezra's name, etc…
3) The animal must be slaughtered according to the Islamic Sharee’ah.
The correct method of slaughtering is as follows:
a) For cows, sheep, and birds: cutting the two jugular veins and the throat.
b) For camels: piercing the hole found at the upper part of chest at the beginning of the neck with a sharp tool.
c) Hunting the animal by a means that is considered as a way of slaughtering in the religion of the hunter (Jew or Christian) such as sending a trained hound/falcon, or by a special gun.
This opinion is supported by the Quranic verse:
Allah Says (what means): {This day [all] good foods have been made lawful, and the food of those who were given the Scripture is lawful for you and your food is lawful for them.} [Quran 5:5]
For more benefit on meat of animals slaughtered by the People of the Book, please refer to Fatawa 82323, 82065, 81234, 393961, 330952, 82899 and 84072.
Allah knows best.