Alexander was born in Portobello in 1873, the sixth of seven children of a local farm servant named Andrew and his wife, Christina. Like his father, his first job was a farm servant, however, by the age of 27, he had become a confectioners vanman. On 9 December 1898, he married Agnes Lock in Musselborough and two children were born of the marriage.
Having spent much of the war working as a warehouseman, Alexander eventually enlisted in 1918 and joined the RAF as a clerk 3rd class on 24 October. Following the Armistice, he went into the RAF reserve on 26 February 1919 and was eventually discharged from service a year later on 30 April.
After the war, Alexander worked as a valve spring inspector and lived in Musselborough until his death in 1959.