Abu Ubaid, the freed slave of Ibn Azhar, reported: I observed Id along with Umar bin al-Khattab (RA) . 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.
Qaza'a related from Abu Sa'id. He said: I heard from him (Abu Sa'id) a hadith which impressed me, and I said to him: Did you hear it from the Messenger of Allah (ﷺ) ? Thereupon he said: (Is it possible) that (I should) say about the Messenger of Allah (ﷺ) that which I have not heard? I heard him saying: It is not proper to fast on two days, Adha and Fitr (at the end) of Ramadan.
Abu Sa'id al-Khudri (RA) reported that the Messenger of Allah (ﷺ) forbade to observe fast on two days the day of Fitr and the day of Sacrifice ('Id-ul-Adha).
Ziyad bin Jubair reported that a person came to Ibn 'Umar (RA) and said: I had taken a vow that I would fast on the day (but it accidentally) synchronises with the day of Adha or the day of Fitr. Thereupon Ibn 'Umar (RA) said: Allah, the Exalted, has commanded fulfilling of the vow, but the Messenger of Allah (ﷺ) has forbidden the observance of fast on this day.