The Messenger of Allah ﷺ used to teach us the tashahhud just as he would teach us a surah from the Quran. He would say, "All blessed greetings, pure prayers are for Allah. Peace be upon you, Prophet, and the mercy of Allah and His blessings. Peace be upon us and upon the righteous servants of Allah. I bear witness that there is no god but Allah, and I bear witness that Muhammad is His servant and His Messenger."
حدثنا محمد بن رمح أنبأنا الليث بن سعد عن أبي الزبير عن سعيد بن جبير وطاوس
كان رسول الله ﷺ يعلمنا التشهد كما يعلمنا السورة من القرآن فكان يقول التحيات المباركات الصلوات الطيبات لله السلام عليك أيها النبي ورحمة الله وبركاته السلام علينا وعلى عباد الله الصالحين أشهد أن لا إله إلا الله وأشهد أن محمدا عبده ورسوله
Muslim narrated it in his Sahih, in the Book of Prayer, Chapter on the Tashahhud in Prayer, hadith no. 403, from Muhammad bin Rumh and others, with this wording.