Abu Huraira (Allah be pleased with him) reported that the Messenger of Allah ﷺ forbade fasting on these two days. 'Id-ul-Adha and 'Id-ul-Fitr. (Using translation from Muslim 1138)  

«أَنَّ رَسُولَ اللَّهِ ﷺ نَهَى عَنْ صِيَامِ يَوْمَيْنِ يَوْمِ الْفِطْرِ وَيَوْمِ الْأَضْحَى»  

"The Messenger of Allah said: 'Fasting is a shield."' (Using translation from Nasāʾī 2224)   

قَالَ رَسُولُ اللَّهِ ﷺ «لَا صَوْمَ فِي يَوْمِ عِيدٍ» *  

I observed Id along with Umar b. al-Khattab (Allah be pleased with him). He came (out in an open space) and prayed and (after) completing it addressed the people and said: The Messenger of Allah ﷺ has forbidden the observing of fast on these two days. One is the day of Fitr (at the end of your fasts), and the second one, the day when you eat (the meat) of your sacrifices. (Using translation from Muslim 1137)  

«إِنَّ هَذَيْنِ يَوْمَانِ نَهَى رَسُولُ اللَّهِ ﷺ عَنْ صِيَامِهِمَا يَوْمُ فِطْرِكُمْ مِنْ صِيَامِكُمْ وَالْأَخَرُ يَوْمٌ تَأْكُلُونَ فِيهِ مِنْ نُسُكِكُمْ» قَالَ أَبُو عُبَيْدٍ ثُمَّ شَهِدْتُ الْعِيدَ مَعَ عُثْمَانَ بْنِ عَفَّانَ فَجَاءَ فَصَلَّى ثُمَّ انْصَرَفَ فَخَطَبَ فَقَالَ إِنَّهُ قَدِ اجْتَمَعَ لَكُمْ فِي يَوْمِكُمْ هَذَا عِيدَانِ فَمَنْ أَحَبَّ مِنْ أَهْلِ الْعَالِيَةِ أَنْ يَنْتَظِرَ الْجُمُعَةَ فَلْيَنْتَظِرْهَا وَمَنْ أَحَبَّ أَنَّ يَرْجِعَ فَلْيَرْجِعْ فَقَدْ أَذِنْتُ لَهُ قَالَ أَبُو عُبَيْدٍ ثُمَّ شَهِدْتُ الْعِيدَ مَعَ عَلِيِّ بْنِ أَبِي طَالِبٍ وَعُثْمَانُ مَحْضُورٌ فَجَاءَ فَصَلَّى ثُمَّ انْصَرَفَ فَخَطَبَ النَّاسَ