He was born in the Ashton upon Mersey district of south Manchester, England, the son of John George Adami, a local hotel proprietor, and his wife, Sarah Ann Ellis Leech.

[3] Elected fellow of Jesus College, Cambridge in 1891, he soon afterwards became head of the pathological department of the Royal Victoria Hospital.

He was elected a Fellow of the Royal Society of Edinburgh in 1898, His proposers were John Batty Tuke, Diarmid Noel Paton, Thomas Richard Fraser and David Berry Hart.

In 1903 Adami proposed two new terms that would be used to classify the neoplasms: lepidic (from λεπις, λεπιδος, meaning a rind, skin, or membrane), applied to characterise the tumors that appeared to be derived from connective tissues, and hylic (from ύΛη, meaning crude undifferentiated material) for tumors that appeared to be derived from connective tissues.

In the present day the term lepidic defines the proliferation of tumor cells along the surface of intact alveolar walls without stromal or vascular invasion.