Alexander was born in Allegheny, Pennsylvania, now a part of Pittsburgh, Pennsylvania. Orphaned in infancy, he was reared by his grandparents and, at the age of 12, became a telegraph boy in Pittsburgh. Edward J. Allen became an early supporter and patron of John W. Alexander, adopting the orphaned Alexander while he worked at the Pacific and Atlantic Telegraph Co. as a young man. Allen brought Alexander to the Allen home at "Edgehill" where Alexander painted various members of the Allen family, including Colonel Allen. His talent at drawing attracted the attention of one of his employers, who assisted him to develop them.