Alexander Nisbet was born in Oldhamstocks, East Lothian, Scotland, son of Margaret Patterson and Captain Alexander Nisbet. He joined the British Royal Navy Medical Service in 1812. He saw active service during the American War (1812-1814). In 1823 he completed a doctorate in medicine at the University of Edinburgh, submitting a dissertation entitled "Pneumonia Typhode". He then began a long and successful career as a surgeon-superintendent serving on seven convict ships transporting convicts from the UK to Australia (1824-1840).