The following is recorded by Ibn Hisham (died 213 H/833 CE) in his sirah (biography) of the Prophet ﷺ:

‘Abdullah ibn Salam ibn al-Harith*, whose name was Al-Husayn before the the Messenger of Allah ﷺ renamed him when he embraced Islam, was a learned rabbi among the Jews. Ibn Ishaq says: It is narrated on the authority of ‘Abdullah ibn Salam [May Allah be Pleased with him] that he said:

“When I heard about the Messenger of Allah ﷺ I knew by his description, name and the time he was expected to appear that he was the one we were waiting for, and I rejoiced greatly thereat. I kept it a secret and did not disclose it to anyone until the Messenger of Allah ﷺ arrived in Medina. When he stayed in Quba’, among the Banu ‘Amr b. ‘Awf a man came with the news while I was pollinating some date palms of mine and my paternal aunt, Khalida bint al-Harith was sitting below.

When I heard the news I cried: ‘Allahu Akbar!’ and my aunt said, ‘Good gracious! By Allah, had you heard about the coming of Moses, son of ‘Imran, you would not have rejoiced more!’ I said, ‘O my aunt! He is, by Allah, the brother of Moses, son of ‘Imran, and follows his religion, being sent with the same mission.’ She asked: ‘O My nephew! Is he the same Prophet we have been told will be sent a short time before the final Hour?” I answered in the affirmative, thereupon she said: ‘Then you have the right (to be happy).’

He added: I then went out to the Messenger of Allah ﷺ and embraced Islam, and returned home and commanded my family to accept Islam, and they did accordingly. I also concealed my conversion to Islam from the Jews. I came to the Messenger of Allah ﷺ and said: ‘No doubt, the Jews are a nation of liars and slanderers, and I wish you would take me into one of your houses and hide me from them. Then ask them about me so that they may tell you the position I hold among them before they know I have become a Muslim. For if they know it beforehand they will utter slanderous lies against me.’ The Prophet made me enter one of his houses; the Jews came and asked him about many things. Then he asked them: ‘What kind of man is Al-Husayn ibn Salam among you?’ They replied, ‘He is our chief and the son of our chief;  our rabbi and our learned man.’ When they said this I emerged and said, ‘O Jews! Fear Allah and accept what He has brought to you. For by Allah you know well that he is the Messenger of Allah. You will find him described in your Torah and even named. I testify that he is the Messenger of Allah, have faith in him and I acknowledge him.’ They accused me of lying and reviled me. On that I said to the Messenger of Allah ﷺ:  ‘Have I not told you, O Messenger Allah, that they are slanderers, inventors of lies, betrayers and wicked?’ I publicly proclaimed my conversion and that of my family, and my aunt Khalida followed suit.”

[Cf. Dr. Muhammad Mahdi al-Sharif, The Prophetic Biography – Sirah of Ibn Hisham, Dar al-Kutub al-Ilmiyah, Beirut, 1434 H/2013 CE, pp.266-267; Alfred Guillaume, The Life of Muhammad: A translation of [Ibn] Ishaq’s Sirat Rasul Allah, Oxford University Press, Karachi, 1987, pp. 240-241]

*The Qur’an refers to him in verse 46:10:

قُلْ أَرَءَيْتُمْ إِن كَانَ مِنْ عِندِ ٱللَّهِ وَكَفَرْتُم بِهِۦ وَشَهِدَ شَاهِدٌۭ مِّنۢ بَنِىٓ إِسْرَٰٓءِيلَ عَلَىٰ مِثْلِهِۦ فَـَٔامَنَ وَٱسْتَكْبَرْتُمْ ۖ إِنَّ ٱللَّهَ لَا يَهْدِى ٱلْقَوْمَ ٱلظَّـٰلِمِينَ

The following explanation of the verse is from Tafsir al-Jalalayn (Qur’an translation in bold italics, tafsir in normal text):

“Say: ‘What do you think?’ Tell me what your state will be. If it (the Qur’an) is from Allah and you reject it, when a witness from the tribe of Israel (‘Abdullah ibn Salam) testifies to its similarity to previous Revelations, affirming that it is from Allah, and so the witness believes while you are too arrogant to believe … ! You are wrongdoers and Allah certainly does not guide wrongdoing people.”

[Jalal al-Din al-Mahalli and Jalal al-Din al-Suyuti, Tafsir al-Jalalayn, translated by Aisha Bewley, Dar al-Taqwa, London, 2007 CE, p. 1079]