This excerpt is taken from Sheikh Muhammad Farooq's book Issues of the Two Eids.
The Eid sermon is Sunnah after the Eid prayer:
The place of the Eid sermon is after the Eid prayer. This has been the consistent practice of the Holy Prophet ﷺ. A detailed discussion on this issue is presented under the title "The Eid prayer is Sunnah before the Eid sermon."
Further Evidence:
❀ Abu Saeed Khudri (may Allah be pleased with him) narrates:
كان النبى صلى الله عليه وسلم يخرج يوم الفطر والأضحى إلى المصلى فأول شيء يبدأ به الصلاة ثم ينصرف فيقوم مقابل الناس والناس جلوس على صفوفهم فيعظهم ويوصيهم ويأمرهم
“The Holy Prophet ﷺ used to proceed towards the Eidgah on the day of Eid al-Fitr and Eid al-Adha (for the Eid prayer), and the first thing he would begin with at the Eidgah was the prayer. After completing the prayer, the Prophet ﷺ would stand facing all the people while they remained seated in their rows, then he would admonish and advise them and command them regarding various matters.”
Reference: Sahih Bukhari, Book of the Two Eids, Chapter: Going out to the Musalla without a pulpit: 956 - Sahih Muslim, Book of Eid Prayers: 889
Fiqh of the Hadith:
(1) Shawkani, may Allah have mercy on him, says:
وأول شيء يبدأ به الصلاة These words are evidence that "offering the Eid prayer before the Eid sermon is Sunnah."
Reference: Nail al-Awtar: 321/3
(2) Sayyid Sabiq states: The Eid sermon is Sunnah after the Eid prayer.
Offering the Eid sermon before the Eid prayer is an innovation:
(1) It is narrated from Tariq bin Shahab that he said:
أول من بدأ بالخطبة يوم العيد قبل الصلاة مروان فقام إليه رجل فقال الصلاة قبل الخطبة فقال قد ترك ما هنالك فقال أبو سعيد أما هذا فقد قضى ما عليه سمعت رسول الله صلى الله عليه وسلم يقول من رأى منكم منكرا فليغيره بيده فإن لم يستطع فبلسانه فإن لم يستطع فبقلبه وذلك أضعف الإيمان
"The first person who started the Eid sermon before the Eid prayer was Marwan bin Hakam. Upon this, a man stood up and said: The Eid prayer is prescribed before the Eid sermon. To this, Marwan said: This Sunnah has been abandoned. (Hearing this) Abu Saeed Khudri (may Allah be pleased with him) said: This man fulfilled his duty. I heard the Messenger of Allah (peace be upon him) say: Whoever among you sees an evil, let him change it with his hand; if he is not able to do so, then with his tongue; and if he is not able to do so, then with his heart—and that is the weakest level of faith."
Reference: Sahih Muslim, Book of Faith, Chapter on the Explanation that Forbidding Evil is Part of Faith: 49
And
Reference: Abu Dawood: 1140, Tirmidhi: 2172, Ibn Majah: 1275, and Musnad Ahmad: 49/3
mention that this man said to Marwan bin Hakam regarding this act against the Sunnah:يا مروان خالفت السنة
"O Marwan! You have opposed the Sunnah."
Fiqh al-Hadith :
After narrating this hadith, Ibn Qudamah writes:
فعلى هذا من خطب قبل الصلاة فهو كمن لم يخطب لأنه خطب فى غير محل الخطبة أشبه ما لو خطب فى الجمعة بعد الصلاة
"According to this hadith, whoever delivers the sermon before the Eid prayer, it is as if he has not delivered the sermon at all, because he has given the sermon at an inappropriate time. It is like giving the Friday sermon after the Friday prayer. (Just as the Friday sermon after the Friday prayer is inappropriate and not permissible, similarly the Eid sermon before the Eid prayer is inappropriate and against the Sunnah)."
❀ Abu Saeed Khudri (may Allah be pleased with him) narrates:
فلم يزل الناس على ذلك حتى خرجت مع مروان وهو أمير المدينة فى أضحى أو فطر، فلما أتينا المصلى إذا منبر بناه كثير بن الصلت، فإذا مروان يريد أن يرتقيه قبل أن يصلي، فجذبته بثوبه فجذبني فارتفع فخطب قبل الصلاة فقلت له غيرتم والله فقال أبا سعيد قد ذهب ما تعلم فقلت ما أعلم خير والله مما لا أعلم فقال إن الناس لم يكونوا يجلسون لنا بعد الصلاة فجعلتها قبل الصلاة
"People always adhered to this Sunnah (performing the Eid prayer and then delivering the Eid sermon) until I went out with the Emir of Madinah, Marwan, on the day of Eid al-Adha or Eid al-Fitr. When we reached the Eidgah, suddenly there was a pulpit there which was built by Kathir bin Salat. So Marwan intended to ascend the pulpit before the Eid prayer, and I pulled him back by his clothes, and he pulled me back. Then in the tug of war, he ascended the pulpit and delivered the sermon before the Eid prayer. I said to him: By Allah! You have changed the (Sunnah) way. He said: Abu Saeed! What you know (the Sunnah) has disappeared. Abu Saeed said: By Allah! What I know is better than what I do not know. Then Marwan excused himself saying: People do not sit for us after the Eid prayer, so I delivered the Eid sermon before the Eid prayer."
Reference: Sahih Bukhari, Book of the Two Eids, Chapter: Going out to the Musalla without a pulpit: 956 - Sahih Muslim, Book of Eid Prayers: 889 - Al-Mughni by Ibn Qudamah: 240/2
Also, the narration which states that the first to precede the Eid prayer with the Eid sermon was Muawiyah (may Allah be pleased with him) is weak.
❀ Ibn Shihab Zahri (may Allah have mercy on him) states:
أول من بدأ بالخطبة قبل الصلاة معاوية
"The first one who started the Eid sermon before the Eid prayer was Muawiyah (may Allah be pleased with him)."
Reference: Musannaf Abd al-Razzaq: 5646 - Its chain is weak
There is tadlis (concealment) by Imam Abd al-Razzaq bin Hammam and Ibn Jurayj in it.