Short answer
When the adhan was taught in a dream to Abdullah ibn Zayd, the Prophet ﷺ told him to teach it to Bilal because Bilal had the stronger and more beautiful voice. Bilal ibn Rabah, a freed Abyssinian slave who suffered for his faith, became the first muezzin of Islam.
The Sunni account, from Sunan Abi Dawud and the seerah books, is that the Prophet ﷺ chose Bilal for the adhan because of his voice, after Abdullah ibn Zayd saw the words of the adhan in a dream in the first years in Madinah.
The four schools agree on this.
Explanation
In the first year or so in Madinah, the Muslims discussed how to call people to prayer. Some suggested a bell like the Christians or a horn like the Jews. Then Abdullah ibn Zayd saw a man in a dream teaching him the words of the adhan. He told the Prophet ﷺ, who said it was a true dream and told him: stand with Bilal and teach him what you saw, so he can call it, because he has a stronger voice than you. Umar then came and said he had seen the same dream.
Bilal ibn Rabah was an Abyssinian, a slave of Umayya ibn Khalaf in Makkah. When he accepted Islam he was tortured on the burning sand with a rock on his chest, and he kept saying "Ahad, Ahad" (One, One). Abu Bakr bought and freed him. Umar later said: Abu Bakr is our master, and he freed our master, meaning Bilal.
So the man who had been tortured for saying Allah is One became the voice that called Madinah to prayer five times a day. He gave the adhan on top of the Kaaba on the day Makkah was conquered. The Prophet ﷺ told him he had heard his footsteps ahead of him in Paradise.
After the Prophet's ﷺ death Bilal went to Syria, and reports say he rarely gave the adhan again. He died there around 20 AH. Read his full life on Bilal ibn Rabah. For the words of the call, see Adhan.
The evidence
Sunan Abi Dawud 499
Grading to be checked... فإنه أندى صوتا منك ...
"For he has a stronger voice than you."
Why Bilal was chosen, graded hasan sahih.
Sahih al-Bukhari 3754
Sahih... أبو بكر سيدنا وأعتق سيدنا ...
"Abu Bakr is our master, and he freed our master."
Umar's words honouring Bilal.
Sahih al-Bukhari 1149
Sahih... سمعت دف نعليك بين يدى في الجنة ...
"I heard the sound of your sandals ahead of me in Paradise."
His rank with the Prophet.
Where the ruling is recorded
- al-Isaba fi Tamyiz al-Sahaba (Ibn Hajar), Entry on Bilal ibn Rabah. His origin, his torture, his freedom and his death in Syria.
- Sirat Ibn Hisham, Account of the beginning of the adhan. The dreams of Abdullah ibn Zayd and Umar.
- Zad al-Ma'ad (Ibn al-Qayyim), Section on his muezzins. Names Bilal as the first of the Prophet's muezzins.
Checked by our team. For a more accurate answer to your own situation, consult a scholar. Quran translation by Sahih International. Hadith Arabic from the standard editions of the six books and the Muwatta, with gradings as recorded there; the English is our own rendering. Spotted a mistake? Tell us.