The museum was founded by Ferenc Széchényi, father of István Széchenyi in November 1802 when he donated his large library and collection of royal coat of arms, maps, artworks and manuscripts to the state.

At first the collection was held in a building near today's University Church. After the foundation of the institution became official in 1808, there was a need for a new building for the museum. The designs were made by the master of Hungarian neoclassical architecture, Mihály Pollack and the construction took place between 1837 and 1847. The museum soon became a national symbol as during the Revolution of 1848-49, the poet Sándor Petőfi held a speech in front of the building (today it is said he recited his famous poem, the Nemzeti Dal, 'national song"). The museum was also used for session by the Upper House of the 1848 Hungarian Parliament.

The statues on the characteristic, neoclassical facade of building were carved by the Austrian sculptor Rafael Monti. The central figure of the group of statues is Pannonia, who offers laurel wreaths to the personifications of science, art and history. The main staircase of the museum is decorated by allegorical frescoes painted by Károly Lotz and Mór Than in 1875.

The English garden of the museum was created by Ármin Petz in 1853. The trees were brought from Margitsziget (Margaret Island), Kiskunlacháza and from the estate of Baron Simon Sina in Gödöllő. The garden has been an important location ever since, not only because of its historical past but as it became a popular park for locals.