Juan Pizarro,[1] brother of Francisco, gave the congregation this land containing the Inca temple. He had received the land in the distribution of lots that took place in October 1534. The congregation was founded that same year, and it was the first Dominican convent in what became Peru. Construction of the first convent building was completed in 1610.[2]

The first prior of the Convent of Santo Domingo was Friar Juan de Olías.[1] He occupied it with a group of Dominican missionaries from Mexico. The convent completely collapsed during the severe damage of the May 12, 1650 Cusco earthquake.[2]

In 1680 construction of the current convent began, financially supported by patrons Diego López de Zúñiga and Antonio de Allende. The architects were Martín Gonzales de los Lagos, Sebastián Martínez and Pedro de Mesa. Part of the choir was built by Francisco Domínguez de Arellano.[2] The convent (or monastery) was completed by addition of the Baroque bell tower in the early 18th century.[2]

The earthquake of 1950 severely affected the bell tower and the apse chapel. These were quickly restored.[2][3]