Salting was born in Sydney, the son of Severin Knud Salting (1806–1865) (in English 'Severin Kanute Salting'), a Dane who had extensive business interests in New South Wales. In 1858 he made a gift of £500 to the University of Sydney to found scholarships to be awarded to students from Sydney Grammar School. George Salting's mother was Louisa Augusta, née Fiellerup.
George Salting was educated locally and then moved with his family to England and studied at Eton College. In 1853 the family returned to New South Wales, and Salting entered the newly founded University of Sydney. There he won prizes for compositions in Latin hexameters in 1855 and 1857, in Latin elegiacs in 1856, 1857 and 1858, and for Latin essays in 1854 and 1856. Salting graduated with a Bachelor of Arts degree in 1857. In 1858 the Salting family again travelled to England; Louisa Salting died there on 24 July 1858. Severin Salting settled in Kent, where he died in 1865. Severin Salting made a large fortune in sheep-farming and sugar-growing which he bequeathed to his son; George Salting inherited a fortune estimated at £30,000 a year.