During and following Muhammad's preaching, converts came from the following three regions throughout the Early Islamic Conquests.
Arabia: The Arabian Peninsula was a very diverse region during Late Antiquity. A large number of Arabs were pagans, following one or more of the various tribal deities. These pagans worshiped at and made pilgrimages to shrines, located usually at oases, called harams. Around these harams, which were usually natural features (such as sacred trees or rocks), towns grew. Due to laws forbidding bloodshed in harams, the towns surrounding them became important commercial centers. By far the most famous of these was Mecca, which was the location of Muhammad's birth. There were also many Jews in Arabia, especially Yemen and various northern towns (such as Khaybar and Yathrib, or Medina). These Jews probably came to Arabia following the Roman destruction of the Temple in Jerusalem. Christians also lived in Arabia in large numbers. Their presence was significant in the northwest, near the Byzantine frontier (at the time of Muhammad, this area was ruled by a Arab client state of the Byzantines, the Ghassanids, who were Hellenized and Christian), and in Yemen, following Byzantine proselytizing.
The Byzantine Empire: The Orthodox Byzantines ruled over a diverse group of subjects. Egypt and the Levant were populated mostly with Christians, though many different sects. The sectarian conflict in Byzantine territory was often bloody. First, the Orthodox Byzantines subscribed to the Dyophysite brand of Christianity, the brand stated as the truth at the Council of Chalcedon in 451 AD. Dyophysites were mainly located in cities--Imperial strongholds of support--and Anatolia, the Balkans, and Greece. In Egypt and the Levant, one would find mostly Monophysites. Jews also lived in the Byzantine Empire, though they were small in number.
The Sassanid Empire: The Sassanid Empire was similar in some respects to the Byzantine Empire. The quasi-state religion, Zoroastrianism, was the religion of the elite. Sassanid social structure was rigid, and the fire temples of Zoroastrianism were mainly located A) on the Iranian Plateau, and B) in the countryside (unable to be reached by poor city folk), though Zoroastrianism was still the major religion of the empire. Mesopotamia, the rich land between Arabia, Syria, and the Zagros Mountains, was a population center for the Sassanids and was where the capital of Ctesiphon was located. Mesopotamia and and Khuzestan (the land of Elam) were home to a large number of Nestorian Christians who fled Byzantium, fearing persecution. Ctesiphon was even the seat of the Nestorian patriarch. (As a side note, Nestorian missionaries traveled very far east. There were Nestorian communities along the Silk Road in Central Asia and in Tang China.)
As I said above, Islam received converts from all of these places. The Islamic Conquests swept through the Near East, but the religion of Islam didn't. It took hold slowly and it was centuries following conquest before Muslims became the majority in places like Egypt and the Levant.
This post was longer than expected; hopefully you found what you were looking for! I am just fascinated by the religions of the Late Antique Near East.