The words said sitting in every prayer
He taught it the way he taught a sūrah of the Qur'an.
التَّحِيَّاتُ الْمُبَارَكَاتُ الصَّلَوَاتُ الطَّيِّبَاتُ لِلَّهِ السَّلاَمُ عَلَيْكَ أَيُّهَا النَّبِيُّ وَرَحْمَةُ اللَّهِ وَبَرَكَاتُهُ السَّلاَمُ عَلَيْنَا وَعَلَى عِبَادِ اللَّهِ الصَّالِحِينَ أَشْهَدُ أَنْ لاَ إِلَهَ إِلاَّ اللَّهُ وَأَشْهَدُ أَنَّ مُحَمَّدًا رَسُولُ اللَّهِ
At-taḥiyyātu lillāhi wa-ṣ-ṣalawātu wa-ṭ-ṭayyibāt. As-salāmu ʿalayka ayyuha-n-nabiyyu wa raḥmatu-llāhi wa barakātuh. As-salāmu ʿalaynā wa ʿalā ʿibādi-llāhi-ṣ-ṣāliḥīn…
“All greetings, prayers and good things are for Allah. Peace be upon you, O Prophet, and the mercy of Allah and His blessings. Peace be upon us and upon the righteous servants of Allah.”
The full narration
Ibn `Abbas reported:The Messenger of Allah (ﷺ) used to teach us tashahhud just as he used to teach us a Surah of the Qur'an, and he would say: All services rendered by words, acts of worship, and all good things are due to Allah. Peace be upon you, O Prophet, and Allah's mercy and blessings. Peace be upon us and upon Allah's upright servants. I testify that there is no god but Allah, and I testify that Muhammad is the Messenger of Allah. In the narration of Ibn Rumh (the words are): "As he would teach us the Qur'an
Source
Ṣaḥīḥ Muslim · 902
- Agreed upon as authentic (al-Bukhārī / Muslim)