The Messenger of Allah ﷺ used to teach us the tashahhud just as he would teach us a surah from the Quran.
حدثنا يحيى بن آدم حدثنا عبد الرحمن بن حميد حدثنا أبو الزبير عن طاوس
كان رسول الله ﷺ يعلمنا التشهد كما يعلمنا السورة من القرآن
Its isnad is sahih. Abdul-Rahman bin Humayd bin Abdul-Rahman Ruasi, with the ra vowelled with damma and the hamza with fatha, lightened, is trustworthy. Ibn Main, Nasai, Ibn Saad, and others declared him trustworthy. The hadith is abridged, 2665.