Foley was born 24 May 1818, at 6 Montgomery Street, Dublin, in what was then the city's artists' quarter. The street has since been renamed Foley Street in his honour. His father was a glass-blower and his step-grandfather Benjamin Schrowder was a sculptor. At the age of thirteen he began to study drawing and modelling at the Royal Dublin Society, where he took several first-class prizes. In 1835 he was admitted as a student in the schools of the Royal Academy in London. He exhibited there for the first time in 1839, and came to fame in 1844 with his "Youth at a Stream". Thereafter commissions provided a steady career for the rest of his life. In 1849 he was made an associate, and in 1858 a full member of the Royal Academy of Art.