The mosque was commissioned by the Greek Mahmud Pasha, the grand vizier of Sultan Mehmet II, who converted to Islam.

This suggests that Mehmet II may have entrusted Mahmud Pasha with developing this district near the commercial heart of the city, just east and north of the area which would become the Grand Bazaar.

The columns holding up the outer porch were originally marble but were replaced by the present stone ones in the 18th century after damage by an earthquake.

The octagonal mausoleum (türbe) of Mahmud Paşa in the grounds of the mosque is dated AH 878 (1473-74 CE) on an inscription at the entrance.

[4] Its exterior is decorated with tiles forming geometric patterns in turquoise and indigo colours, a feature which is unique in Ottoman architecture in Istanbul.

The külliye of Mahmut Pasha included, in addition to the mosque and the mausoleum, a hammam (public bathhouse), a han or caravanserai, a madrasa, an imaret (soup kitchen), a mahkeme (courtroom), and a mekteb (elementary school).

The building contributed to the revenues of the mosque's waqf foundation by collecting rent from the shops and offices which occupied its many rooms (which at one point numbered 167).