The predecessor of the Sport Arena, the Budapest Sports Hall designed by István Kiss, was inaugurated on February 12, 1982. The building was modeled on the Leninrgad Jubilee Sports Palace, although it was slightly larger. It received 12,500 spectators. In December 1999, the Budapest Sports Hall became a fixture during the Christmas market. The disaster shocked the public as the BS was the only indoor building that could accommodate thousands of people, hosting many music concerts, cultural events, and sports events. The building was completely burnt down and there was no possibility of its restoration, so a new sports hall was begun and its construction began on June 30, 2001. The ceremony was handed over on March 13, 2003.

The opening ceremony took place on March 14 and ended with a gigantic classical music concert. The Budapest Sportarena has been named after László Papp since May 28, 2004.