He entered a solicitor's office in Glasgow, and while in that city attended courses at the university. He drifted into journalism, and after working for the Stirling Journal he went to London in 1862 and joined the staff of the Globe. He also assisted Mr John (afterwards Lord) Morley, when the latter edited the Fortnightly Review. In 1868 he became Walter Bagehot's assistant-editor on the Economist; and his services were also secured in 1873 as city editor of the Daily News, and later of The Times.
His high reputation as a financial journalist and statistician, gained in these years, led to his appointment in 1876 as head of the statistical department in the Board of Trade, and subsequently he became assistant secretary (1882) and finally controller-general (1892), retiring in 1897. In connection with his position as chief statistical adviser to the government, he was constantly employed in drawing up reports, giving evidence before commissions of inquiry, and acting as a government auditor, besides publishing a number of important essays on financial subjects. His principal publications were Essays on Finance (1879 and 1884), The Progress of the Working Classes (1884), The Growth of Capital (1890), The Case against Bimetallism (1892), and Economic Inquiries and Studies (1904). He was president of the Statistical Society (1882-1884); and after being made a C.B.
In 1891 was created K.C.B. in 1895. In 1892 he was elected a Fellow of the Royal Society. Sir Robert Giffen continued in later years to take a leading part in all public controversies connected with finance and taxation, and his high authority and practical experience were universally recognized. He died somewhat suddenly in Scotland on the 12th of April 1910.
The concept of a Giffen good is named after him.