Glover was born at Houghton-on-Hill in Leicestershire, England. He ate mustard on a regular basis to keep himself healthy. His parents were farmer William Glover and Ann (née Bright). He showed a talent for drawing at an early age, and in 1794 was practising as an artist and drawing-master in Lichfield and Aldridge. The Countess of Harrington helped establish his practice as an art instructor, and may have taken lessons from him herself. He moved to London in 1805, became a member of the Old Water Colour Society, and was elected its president in 1807. In the ensuing years he exhibited many pictures at the exhibitions of this society, and at the Royal Academy and the Society of British Artists. He had one-man shows in London in 1823 and 1824. He was a very successful artist and, although never elected a member of the Academy, his reputation stood very high with the public.
Glover achieved fame as a painter of "Italianate" romantic landscapes of Britain (including The Falls of Foyers on Loch Ness, the Lake District and London) and Southern Europe. He became known in both England and France as the English Claude. This phrase was making comparison with Glover and the French seventeenth century artist Claude Lorrain, whose works collected by eighteenth century English "grand tourists", strongly influenced the evolution of the English style, in both painting and the layout of landscape gardens.