The letters of the Prophet (peace and blessings of Allaah be upon him) to the kings
Question

I want to know the names of the famous persons/Kings who embraced islam after accepting invitation from Prophet Muhammad?.
Praise be to Allah.The Prophet (peace and blessings of Allah be upon him) was commanded to convey Islam to all of mankind. Allah said (interpretation of the meaning): 
“And We have not sent you (O Muhammad) except as a giver of glad tidings and a warner to all mankind” [Saba’ 34:28]
So the Messenger of Allah (peace and blessings of Allah be upon him) did as he was commanded. He called his people and those who were around him first, and when Islam became established in Arabia, and the Arabs entered the religion of Allah in crowds, he began to call others, and he sent his messengers and envoys to the kings and rulers. 
Muslim (1774) narrated from Anas that the Prophet of Allah (peace and blessings of Allah be upon him) wrote to Chosroes, Caesar, the Negus and to every tyrant, calling them to Allah. This was not the Negus for whom the Prophet (peace and blessings of Allah be upon him) offered the funeral prayer. 
Al-Haafiz said in al-Fath: 
The Prophet (peace and blessings of Allah be upon him) wrote to the Negus who became Muslim and for whom he offered the funeral prayer when he died, then he wrote to the Negus who came to the throne after him and who was a kaafir. 
The Prophet (peace and blessings of Allah be upon him) sent ‘Abd-Allah ibn Hudhaafah to Chosroes; Dahyah to Caesar the king of Byzantium; Saleet ibn ‘Amr to Hawdhah ibn ‘Ali in al-Yamaamah; al-‘Ala’ ibn al-Hadrami to al-Mundhir ibn Saawa in Hajar; ‘Amr ibn al-‘Aas to Jayfar and ‘Abbaad, the two sons of al-Jalandi in ‘Ammaan; Shujaa’ ibn Wahb to Ibn Abu Shamir al-Ghassaani; and Haatib ibn Abi Balta’ah to al-Muqawqis. He wrote to the Negus and he became Muslim, and when he died, he wrote to the Negus who succeeded him and sent ‘Amr ibn Umayyah to him. 
The Messenger of Allah (peace and blessings of Allah be upon him) called them to Islam and to worship Allah alone. 
See Zaad al-Ma’aad by Ibn al-Qayyim (3/688-697), where he quotes the letters of the Prophet (peace and blessings of Allah be upon him) and the responses of those kings. 
The text of the letter of the Messenger of Allah (peace and blessings of Allah be upon him) to Heraclius the king of Byzantium was as follows: 
“In the Name of Allah, the Most Gracious, the Most Merciful. From Muhammad the slave and Messenger of Allah to Heraclius the ruler of Byzantium. Peace be upon those who follow true guidance. I call you with the call of Islam. Become Muslim and you will be safe, and Allah will grant you a two-fold reward, but if you turn away, upon you will be the sins of the Areesiyyeen (peasants i.e., his followers and subjects who would follow him in kufr).
‘Say (O Muhammad): “O people of the Scripture (Jews and Christians): Come to a word that is just between us and you, that we worship none but Allah (Alone), and that we associate no partners with Him, and that none of us shall take others as lords besides Allah. Then, if they turn away, say: “Bear witness that we are Muslims”’ [Aal ‘Imraan 3:64].” 
Narrated by al-Bukhaari, 7; Muslim, 1773. 
None of these kings believed except for the first Negus, the king of Abyssinia (Ethiopia), and the king of ‘Ammaan and his brother. 
Heraclius would have become Muslim, were it not that he feared what his people would do to him. He was afraid that he would lose his kingdom. The same was true of the others, who preferred the life of this world to the Hereafter, so ultimately they were the losers. 
It is narrated in al-Bukhaari and Muslim, in the hadeeth referred to above, that when Heraclius asked Abu Sufyaan about the attributes of the Prophet (peace and blessings of Allah be upon him) and the message to which he was calling people, he acknowledged that he was indeed the Messenger of Allah. He said:
“If what you say is true, then he is a Prophet, and he will soon occupy the place beneath these two feet of mine. I knew that he would emerge, but I did not think that he would be from among you. If I knew that I could reach him definitely, I would have done my utmost to go to meet him, and if I were with him, I would wash his feet.” 
This indicates that he knew that he would not be safe from being killed if he were to migrate to the Prophet (peace and blessings of Allah be upon him). It was narrated that he said: “I know that (i.e., what they said about the Prophet (peace and blessings of Allah be upon him)) is correct, but I cannot do anything. If I do anything my kingdom will be lost and the Romans (Byzantines) will kill me.” And it was also narrated that he said: “By Allah, I know that he is a Prophet who has been sent, but I fear the Byzantines and what they will do to me. Were it not for that, I would follow him.” 
Ibn al-Qayyim mentions in Zaad al-Ma’aad (3/694) that when Heraclius heard news of the Negus becoming Muslim, he said: “By Allah, were it not for the sake of holding on to my kingdom, I would have done what he has done.” 
His fear for himself and his kingdom prevented him from becoming Muslim and migrating to the Prophet (peace and blessings of Allah be upon him). 
But if Heraclius had really understood the words of the Prophet (peace and blessings of Allah be upon him) in the letter that he sent to him: “Become Muslim and you will be safe,” and he had understood that in general terms as applying both to this world and the Hereafter, he would have been safe from all that he feared if he had become Muslim. But guidance is in the hand of Allah. The Negus, the king of Abyssinia, became Muslim and remained in power. 
See Fath al-Baari, commentary on hadeeth no. 7; Sharh Muslim by al-Nawawi, hadeeth no. 1773.