Harrod married Wilhelmine "Billa" Cresswell (1911–2005), step-daughter of General Sir Peter Strickland, in 1938. One of their sons was Dominick Harrod, an economics correspondent for the BBC.
Born in London he attended St Paul's and then Westminster School. Harrod attended New College in Oxford on a history scholarship. After a brief period in the Artillery in 1918 he gained a first in "literae humaniores" in 1921, and a first in modern history the following year. Afterwards he spent some time in 1922 at King's College, Cambridge. It was there that he met and befriended Keynes.
At the 1945 General Election he stood as Liberal candidate for Huddersfield and finished third.
After the death of his Cambridge friend and colleague, the Economist John Maynard Keynes, in 1946, Harrod and Austin Robinson wrote a lengthy obituary of Keynes for The Economic Journal. At the encouragement of Geoffrey Keynes, Harrod then undertook the task of writing a major biography of Keynes. The Life of John Maynard Keynes was published to widespread acclaim in 1951, at a time when most of Keynes's family and friends were still alive.
After moving back to Oxford, he became a Student (i.e., Fellow) and Tutor in economics at Christ Church. He held the fellowship in modern history and economics until 1967. He remained in contact with Keynes until Keynes's death in 1946, and was later his biographer (1951). Harrod was additionally a Fellow at Nuffield College 1938 to 1947 and from 1954 to 1958.
With the post-war influence of so-called Keynesian economics and then challenges to it, cultural interest in the Bloomsbury Group, and the publication of thirty volumes of The Collected Writings of John Maynard Keynes in the 1970s and 1980s, high interest in Keynes's life lead to further biographies, most prominently by Robert Skidelsky and Donald Moggridge, and to detailed studies such as by Donald Markwell on Keynes and international relations. These works have corrected and added details to the Keynes depicted by Harrod, and Skidelsky in particular has contrasted his account of Keynes with what he has depicted as Harrod's hagiography.
During the Second World War, he was briefly in Winston Churchill's "S-branch" – a statistical section within the Admiralty.