BSE first opened for business in 1864 in the Pesti Lloyd building on the banks of the Danube. It moved to the Bourse Palace building on Szabadság tér in 1905, where it kept operating until the Hungarian government dissolved the stock exchange in 1948.

Following the change of regime, the bourse resumed its operations in the Trade Center building on Váci utca, before moving to Vörösmarty tér in 1992. In 2007, after the building was purchased by a developer, the bourse moved into the former Herczog Palace on Andrássy út.