The nine-storey building at number 32 Gran Vía has been bought up by Pontegadea, an investment company belonging to the Galician fashion tycoon, the firm said in a statement.
The move will see Ortega become the landlord of Spanish fashion brands including Spain's Mango and Swedish clothes retailer H&M.
Among the tenants at the building dating from 1924 will also be the Irish high-street fashion store Primark, set to open its largest store in Spain at the location.
The cost of the deal involving the 36,376-square-metre (392,000 square-foot) building has not been released, but Spanish media are reporting a figure of €400 million ($450 million).
Amancio Ortega, the founder of Spanish clothing conglomerate Inditex, which owns the hugely popular clothing stores Zara, Massimo Dutti and Pull & Bear, among others, is listed as the fourth richest man in the world by Forbes magazine with his wealth listed at $63.1 billion.
The famously media-shy Ortega opened his first Zara boutique in 1975 after leaving school at 13.
He now heads up a fashion empire with over 6,570 stories around the world and an estimated 133,400 employees.