Is it permissible to fast on the days of Eid?

The days of Eid are among the foremost days on which fasting is prohibited. It is considered tahriman makruh (strictly discouraged and close to forbidden) to fast on the first day of Eid al-Fitr and on all four days of Eid al-Adha. (Mevsılî, el-İhtiyâr, 1/125-126; Ibn Abidin, Reddü’l-muhtâr, 2/375) The reason fasting is not allowed and is discouraged on these days is because Eid days are meant to be days of eating, drinking, and joy. Eid al-Fitr is regarded as a “general iftar banquet” following a month of fasting for Allah, and for this reason it is called “Fitr Eid” (the Eid of breaking the fast). The first day of Eid al-Fitr signifies the breaking of the Ramadan fast. To fast on such a communal day of breaking the fast would mean not participating in Allah’s banquet, which is clearly inappropriate. The days of Eid al-Adha, when sacrifices are offered for Allah, are also days of feasting. The Prophet (peace be upon him) stated that the days of Tashreeq are days of eating, drinking, and remembering Allah. (Muslim, Sawm, 144 [1141])

Source: T.C. Diyanet İşleri Başkanlığı, Din İşleri Yüksek Kurulu