Born in 1894 in Denham, Buckinghamshire, Nicholson was the son of the painter Sir William Nicholson and Mabel Pryde, and the brother of Nancy Nicholson. The family moved to London in 1896 and Nicholson was educated at Tyttenhangar Lodge Preparatory School, Seaford, Heddon Court, Hampstead and then as a boarder at Gresham's School, Holt, Norfolk. He trained as an artist at the Slade School of Fine Art from 1910?C1914, where he was a contemporary of Paul Nash, Stanley Spencer, Mark Gertler, and Edward Wadsworth.
Nicholson was married three times: firstly to Winifred Roberts (married 5 November 1920 at St. Martin-in-the-Fields Church, London; divorced 1938) with whom he had three children, a son Jake in June 1927, a daughter Kate in July 1929 (who later became an artist herself) and a son Andrew in September 1931. His second marriage was to fellow artist Barbara Hepworth (married 17 November 1938 at Hampstead Register Office; divorced 1951) with whom he had triplets, two daughters Sarah and Rachel and a son Simon in 1934 and third to Felicitas Vogler, a German photographer (married July 1957; divorced 1977).