The National Gallery of Art was created by a joint resolution of
Congress on March 17, 1937, and dedicated on March 17, 1941

The National Gallery of Art was conceived and given to the people of the United States by Andrew W. Mellon (1855–1937). Mellon was a financier and art collector from Pittsburgh who came to Washington in 1921 to serve as secretary of the treasury. During his years of public service he came to believe that the United States should have a national art museum equal to those of other great nations.
In 1936 Mellon wrote to President Franklin D. Roosevelt offering to donate his superb art collection for a new museum and to use his own funds to construct a building for its use. With the president’s support, Congress accepted Mellon’s gift, which included a sizable endowment, and established the National Gallery of Art in March 1937. Construction began that year at a site on the National Mall along Constitution Avenue between Fourth and Seventh Street NW, near the foot of Capitol Hill.
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Construction was completed by December 1940, and works of art were installed in the new galleries over the following months. The National Gallery of Art was dedicated on March 17, 1941, with Paul Mellon presenting the museum on behalf of his father, and President Franklin D. Roosevelt accepting the gift for the nation.
FROM http://www.nga.gov/content/ngaweb/about.html

FDR’s Speech on the Dedication of the National Gallery of Art~
http://www.nga.gov/content/ngaweb/audio-video/audio/west-building-dedication-president-fdr.html
Highlights from the collection~
http://www.nga.gov/content/ngaweb/Collection/highlights.html
75th anniversary programs~
http://www.nga.gov/content/ngaweb/about/seventy-fifth-anniversary.html