He studied Mathematics and Physics at the University of Edinburgh graduating BSc in 1887 and gaining a doctorate (DSc) in 1888. He had been assisting in lectures in Natural Philosophy (Physics) since 1883 and became a formal lecturer in 1892. In 1907 he received a professorship at University College, Dundee.
In 1887 he was elected a Fellow of the Royal Society of Edinburgh. His proposers were Peter Guthrie Tait, Sir Thomas Muir, George Chrystal, and Alexander Crum Brown. He was awarded the Society's Makdougall-Brisbane Prize for 1896–1898, and served as the Society's Vice President from 1919 to 1922. He was President of the Edinburgh Mathematical Society 1896/97. He was an Invited Speaker of the ICM in 1912 at Cambridge, UK. 
He retired in 1942 and died at Ninewells Hospital on 2 June 1946.
His position was filled by Prof George Dawson Preston.
In 1891 he married Jessie Isabella Dott (d.1927).
- O'Connor, John J.; Robertson, Edmund F., "William Peddie", MacTutor History of Mathematics archive, University of St Andrews.
- Peddie, William (1888). On the conduction of electricity through liquids (Thesis). University of Edinburgh.
- "Peddie, Dr. William". Who's Who: 1929. 1919.
- Biographical Index of Former Fellows of the Royal Society of Edinburgh 1783–2002 (PDF). The Royal Society of Edinburgh. July 2006. ISBN 0 902 198 84 X.
- "A mechanism for the solution of an equation of the nTH degree by William Peddie". Proceedings of the Fifth International Congress of Mathematicians (Cambridge, 22—25 August 1912). vol. 1. Cambridge University Press. 1913. pp. 399–402.