McLeod was born in Aberdeen, Scotland, on 23 December 1929.[2] He was educated at Aberdeen Grammar School; the University of Aberdeen, where he took a first in Mathematics and Natural Philosophy in 1950; and Christ Church, Oxford, where he took a first in Mathematics in 1952. He was a Harmsworth Senior Scholar at Merton College, Oxford, from 1955 to 1956.[3] He obtained his PhD in 1959 under the supervision of Edward Charles Titchmarsh at the University of Oxford.[4]
He was a junior lecturer in Mathematics at the University of Oxford from 1956 to 1958, and a lecturer in mathematics at the University of Edinburgh from 1958 to 1960. He then returned to Oxford to take up a Fellowship in Pure Mathematics at Wadham College.[3] He remained in Oxford until 1988, becoming a university lecturer in 1970, and a senior research fellow of the Science and Engineering Research Council from 1986 to 1991.[5] In 1988 McLeod took up a professorship at the University of Pittsburgh, where he remained until his retirement in 2007.[6]
McLeod married Eunice Third in 1956; they had three sons and a daughter.[5] He died in England on 20 August 2014, aged 84.[6]