Hadith: The Messenger of Allah (may Allah’s peace and blessings be upon him) used to teach us the Tashahhud just as he teaches us a Sūrah from the Qur’an

عن ابن عباس رضي الله عنهما ، أنه قال: كان رسول الله صلى الله عليه وسلم يعلمنا التشهد كما يعلمنا السورة من القرآن فكان يقول: «التحيَّات المباركات، الصَّلَوَاتُ الطَّيِّبَاتُ لله، السلام عليك أيها النبي ورحمة الله وَبَرَكَاتُهُ، السلام علينا وعلى عباد الله الصالحين، أشهد أَنْ لَا إِلَهَ إِلَّا اللهُ، وأشهد أنَّ محمَّدا رسول الله» وفي رواية ابن رُمْحٍ كما يُعلِّمنا القرآن.
[صحيح] - [رواه مسلم]

Ibn ‘Abbās (may Allah be pleased with him) reported: The Messenger of Allah (may Allah’s peace and blessings be upon him) used to teach us the Tashahhud just as he used to teach us a Sūrah from the Qur’an. He used to say: "All blessed greetings and good prayers are due to Allah; peace be upon you, O Prophet, and the mercy of Allah and His blessings; peace be upon us and upon the righteous slaves of Allah. I bear witness that none has the right to be worshiped but Allah and I bear witness that Muhammad is His slave and Messenger)." In another narration by Ibn Rumh: “As he used to teach us the Qur’an.”
[Authentic hadith] - [Narrated by Muslim]

Explanation

The Hadīth presents the wording of the Tashahhud and informs that the Prophet (may Allah's peace and blessings be upon him) was keen to teach it to them as he would teach them the verses of the Qur’an. The Tashahhud reads: "All blessed greetings and good prayers are due to Allah; peace be upon you, O Prophet, and the mercy of Allah and His blessings; peace be upon us and upon the righteous slaves of Allah. I bear witness that none has the right to be worshiped but Allah and I bear witness that Muhammad is His slave and Messenger." It is similar to the famous wording reported by Ibn Mas‘ūd (may Allah be pleased with him) except for the addition of the word ‘al-mubārakāt’ (blessed) and the omission of the conjunction ‘and’ from the two subsequent words. It is from the Sunnah to use the various reported wordings of the Tashahhud in separate occasions.