Shaykh Bin Baaz, rahimahullah, said:
“It is narrated that the Prophet (peace be upon him) and a group of the Companions (may Allah be pleased with them) used to recite Takbir following each of the five Salahs from Fajr (Dawn) Prayer on the day of `Arafah until the `Asr (Afternoon) Prayer on the thirteenth day of Dhul-Hijjah. This is applied to those who do not perform Hajj.” End quote. [Reference]
Ibn Rajab, rahimahullah, said:
؛ فاتفق العلماء على أنه يُشرع التكبير عقيبَ الصلوات في هذه الأيام في الجملة،
” …The scholars have come to the agreement in general that it is legislated to perform takbir after the five daily prayers during these days…”. End quote. [Fathul Baari, Ibn Rajab’s explanation of Saheeh al-Bukhaari]
A Note: Ash-Shaykh Bin Baaz, Shaykh Muhammad bin Saalih al-Uthaymeen, and Shaykh Saalih al-Fawzaan see that a person should utter this takbir that is done at the end of the obligatory prayer once he completes saying istighfar three times and after saying, “Allahumma Anta as-Salaam wa Minka as-Salaam…”.
AbdulFattaah Bin Uthman