Imam al-Shafi'i (may Allah have mercy on him) said: "Both of them (the two surahs) are written in the Mushaf that was compiled in the time of Sayyiduna Abu Bakr (may Allah be pleased with him); then it remained with Sayyiduna Umar (may Allah be pleased with him), then with Sayyidah Hafsah (may Allah be pleased with her); then Sayyiduna Uthman (may Allah be pleased with him) united all the people upon it. Both of them are part of the Book of Allah, and I love to recite them in my prayer."
Zirr bin Hubaysh (may Allah have mercy on him) said: I asked Ubayy bin Ka'b (may Allah be pleased with him) about the Mu'awwidhatayn, and he said: I asked the Messenger of Allah (peace and blessings be upon him) about the Mu'awwidhatayn, and he (peace and blessings be upon him) said: "It was said to me, so I said it."
"So we say just as the Messenger of Allah (peace and blessings be upon him) said."
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصلاة / 4044