Anas reported that the Messenger of Allah, may Allah bless him and grant him peace, said, "As-Salam (peace) is one of the Names of Allah Almighty which Allah has placed in the earth. Therefore give the greeting among yourselves."  

قَالَ رَسُولُ اللهِ ﷺ إِنَّ السَّلامَ اسْمٌ مِنْ أَسْمَاءِ اللهِ تَعَالَى وَضَعَهُ اللَّهُ فِي الأَرْضِ فَأَفْشُوا السَّلامَ بَيْنَكُمْ  

Ibn Mas'ud said, " They were doing the prayer with the Prophet, may Allah bless him and grant him peace, and someone said, 'Peace be upon Allah.' When the Prophet, may Allah bless him and grant him peace, finished the prayer, he said, 'Who said "Peace be upon Allah"? Allah is Peace. Rather say, "Greetings belong to Allah and good words and prayers. Peace be upon you, O Prophet and the mercy of Allah and His blessings. Peace be upon us and upon all the right-acting slaves of Allah. I testify that there is no god but Allah and I testify that Muhammad is His slave and Messenger."'"  

عَنِ ابْنِ مَسْعُودٍ قَالَ كَانُوا يُصَلُّونَ خَلْفَ النَّبِيِّ ﷺ قَالَ الْقَائِلُ السَّلاَمُ عَلَى اللهِ فَلَمَّا قَضَى النَّبِيُّ ﷺ صَلاَتَهُ قَالَ مَنِ الْقَائِلُ السَّلاَمُ عَلَى اللهِ؟ إِنَّ اللَّهَ هُوَ السَّلاَمُ وَلَكِنْ قُولُوا التَّحِيَّاتُ لِلَّهِ وَالصَّلَوَاتُ وَالطَّيِّبَاتُ السَّلاَمُ عَلَيْكَ أَيُّهَا النَّبِيُّ وَرَحْمَةُ اللهِ وَبَرَكَاتُهُ السَّلاَمُ عَلَيْنَا وَعَلَى عِبَادِ اللهِ الصَّالِحِينَ أَشْهَدُ أَنْ لاَ إِلَهَ إِلاَّ اللَّهُ وَأَشْهَدُ أَنَّ مُحَمَّدًا عَبْدُهُ وَرَسُولُهُ قَالَ وَقَدْ كَانُوا يَتَعَلَّمُونَهَا كَمَا يَتَعَلَّمُ أَحَدُكُمُ السُّورَةَ مِنَ الْقُرْآنِ