He studied chemistry under Thomas Graham and Alexander William Williamson and mathematics under Augustus De Morgan.

[3] In 1854 Guthrie went to Heidelberg to study under Robert Bunsen and then in 1855 obtained a PhD at the University of Marburg under Adolph Wilhelm Hermann Kolbe.

[6][7] In 1860 Guthrie was elected a Fellow of the Royal Society of Edinburgh, his proposer being Lyon Playfair.

[9] Guthrie was later a professor at the Royal School of Mines in London, where he mentored the future experimental physicist C. V. Boys.

He also mentored John Ambrose Fleming and was instrumental in turning his interest from chemistry to electricity.