Josiah Forshall was born at Witney, Oxfordshire, the eldest son of Samuel Forshall. He received education at the grammar schools of Exeter and Chester, and in 1814 entered Exeter College, Oxford. He graduated BA in 1818, taking a first class in mathematics and a second in literae humaniores. He became MA in 1821, and was elected fellow and tutor of his college.
Forshall was appointed an assistant librarian in the manuscript department of the British Museum in 1824, and became keeper of that department in 1827. In 1828 he was elected a Fellow of the Royal Society.
In 1828 Forshall was appointed secretary to the Museum, and in 1837 resigned his keepership in order to devote himself exclusively to his secretarial duties. He was examined before the select committee appointed to inquire into the Museum in 1835-6, and made revelations on the subject of patronage.
About 1850 Forshall retired from the museum on account of ill-health. After his resignation he lived in retirement, spending much of his time, until his death, at the Foundling Hospital, of which he had been appointed chaplain in 1829. He died at his house in Woburn Place, London, in 1863, after undergoing a surgical operation