Born in Ayrshire in 1858, Henry studied at the Glasgow School of Art and attended informal classes at William Macgregor's studio. Probably his most formative period artistically was spent with fellow Glasgow Boys James Guthrie, E. A. Walton and Joseph Crawhall painting at Brig o'Turk, Roseneath and Cockburnspath (1881 - 1884). There he painted rural scenes in fresh, natural colours, using the square-brush technique favoured by their mentor Jules Bastien-Lepage.
In 1885 he met E. A. Hornel in 1885 leading to a change in style in his art. He became more concerned with brighter colours and decorative pattern and in 1889 he painted one of the masterpieces of the group in this new style, 'A Galloway Landscape'. He later collaborated with Hornel on another major picture, 'The Druids', which took Europe by storm.
In 1893 Henry and Hornel set off for Japan, financed by Alexander Reid, resulting in some of their finest work. Henry's Japanese period is mostly represented by watercolours, as many of his oil were destroyed on the journey home.