Sayyiduna Ibn Abbas and Sayyiduna Jabir bin Abdullah (may Allah be pleased with them both) both said that there was no adhan on the day of Eid al-Fitr or the day of Eid al-Adha. Then, after some time, I asked him about it, and he said: Sayyiduna Jabir bin Abdullah al-Ansari (may Allah be pleased with him) informed me that on the day of Eid al-Fitr, when the imam comes out and after he comes out, there is no adhan and no iqamah.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب صلاة العيدين / 6165
Ata (may Allah have mercy on him) reports that Sayyiduna Abdullah bin Abbas (may Allah be pleased with them both) sent him to Sayyiduna Abdullah bin al-Zubayr (may Allah be pleased with them both) when allegiance was first given to him, (with the message) that the adhan used not to be given for the prayer on the day of Eid al-Fitr, so do not give the adhan for it. So Sayyiduna Abdullah bin al-Zubayr (may Allah be pleased with them both) did not give the adhan for it. Along with that, he also sent him (the message): "The sermon is only after the prayer, for that is what used to be done." He said: So Sayyiduna Abdullah bin al-Zubayr (may Allah be pleased with them both) led the prayer before the sermon.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب صلاة العيدين / 6166
Sayyiduna Jabir bin Samurah (may Allah be pleased with him) said: I prayed the Eid prayer with the Prophet (peace and blessings be upon him) many times without adhan or iqamah.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب صلاة العيدين / 6167