The directors of the two galleries have fixed on 1900 as the date of the beginning of modern art. At present the collections overlap slightly; the Tate - traditionally the home of international modern art - has some late 19th-century pieces and the National Gallery has some early 20th-century paintings.
More than 60 works by non-British artists, including Picasso, Van Gogh, Monet and Matisse, will be lent by one gallery to the other for an experimental period of four years.
Twentieth-century paintings moving from the National to the Tate include Picasso's Cubist work Fruit Dish, Bottle and Violin (1914) and Monet's monumental Water Lilies. Meanwhile Van Gogh's Farms near Auvers (1890), painted two months before his suicide, and Gaugin's Tahitian work Faa Theihe (1898) and other works will travel from the Tate to strengthen the National's collection of those and other post-Impressionist artists.
"It seems to us very important that the collections of this country are where the public expect them to be," Neil MacGregor, director of the National Gallery, said. The changeover will take place next spring.
The loans of 14 National Gallery works and 52 Tate works were organised in a spirit of co-operation, Mr MacGregor and the Tate's director, Nicholas Serota, said.
The last attempt to rationalise the collections was in 1927, when 1870 was established as the beginning of the modern era.
The Tate will continue to hold its British collection, which dates from the 16th century.Reuse content