“The Prophet — may Allah’s peace and blessings be upon him — on the day of Fitr would not go out until he had eaten, and on the day of Naḥr would not eat until he returned.”

Narrated by Aḥmad (No. 22983, the wording is his), al-Tirmidhī (No. 542), and Ibn Mājah (No. 1756), from the ḥadīth of Buraydah ibn al-Ḥusayb, may Allah be pleased with him.
Aḥmad added in another narration (No. 22984): “He would eat from his sacrificial animal.”
Authenticated in Ṣaḥīḥ al-Jāmi‘ (No. 4845) and al-Ta‘līqāt al-Ḥisān (No. 2801).

Brief Explanation of the Hadith

The Prophet — may Allah’s peace and blessings be upon him — was keen to manifest the rites of Islam during the ʿĪd days and to explain to his Companions the rulings and etiquettes that Allah prescribed for them, including those related to eating before and after the ʿĪd prayer.
In this ḥadīth, Buraydah ibn al-Ḥusayb, may Allah be pleased with him, reports that among the Prophet’s guidance on the day of ʿĪd al-Fitr was that he would not go out for the ʿĪd prayer until he had eaten, thereby manifesting the breaking of the fast and distinguishing it from a day of fasting so that it would not be mistaken as a continuation of the fast. It was also his practice to eat an odd number of dates.
As for the day of ʿAḍḥā, the Prophet’s — may Allah’s peace and blessings be upon him — guidance was that he would not eat until he returned from the prayer, so that the first thing he ate would be from his sacrificial animal, thereby manifesting the rite of sacrifice and expressing gratitude to Allah for the sacrificial ordinance. This (practice) applies specifically to those who have a sacrifice to offer. As for those who do not have a sacrifice, it is not recommended for them to refrain from eating before the prayer.
The ḥadīth also indicates the importance of preventing confusion in acts of worship and distinguishing them, so that their rulings do not become conflated.