The 81 year old died of a heart attack on Wednesday, while on a visit to Saudi Arabia.
Tantawi was the head of Egypt’s most prestigious seat of Islamic learning, al-Azhar.
The organisation runs schools and universities across Egypt, as well as sending scholars to teach in other Muslim countries.
His deputy will take charge, before President Hosni Mubarak appoints a new head.
Known for his liberal views, he took charge of al-Azhar in 1996. During his tenure, he represented the more moderate side of Islam – such as opposing the wearing of the full veil or ‘niqab’.
Last year, he banned the practice in schools run by the organisation.