Ward was born in New York City. He received his Ph.D. from Caltech in 1928, with a dissertation entitled The Foundations of General Arithmetic; his advisor was Eric Temple Bell. He became a research fellow at Caltech, and then in 1929 a member of the faculty; he remained at Caltech until his death in 1963. Among his doctoral students was Robert P. Dilworth, who also became a Caltech professor. Ward is the academic ancestor of over 500 mathematicians and computer scientists through Dilworth and another of his students, Donald A. Darling.
Ward's research interests included the study of recurrence relations and the divisibility properties of their solutions, diophantine equations including Euler's sum of powers conjecture and equations between monomials, abstract algebra, lattice theory and residuated lattices, functional equations and functional iteration, and numerical analysis. He also worked with the National Science Foundation on the reform of the elementary school mathematics curriculum, and with Clarence Ethel Hardgrove he wrote the textbook Modern Elementary Mathematics (Addison-Wesley, 1962).
Ward's works are collected in the Caltech library. A symposium in his memory was held at Caltech on November 21–22, 1963. Ward quasigroups are named after him, following his paper on alternative set of group axioms. 
- "New York, New York City Births, 1846-1909," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:2WWG-V9Y : 11 February 2018), Henry Morgan Ward, 20 Aug 1901; citing Manhattan, New York, New York, United States, reference cn 32514 New York Municipal Archives, New York; FHL microfilm 1,983,307.
- "Prof. Ward of Caltech Dies at 61", Los Angeles Times, June 27, 1963.
- "Dr. Ward, 61, Dies; Caltech Theoretician". Pasadena Independent. June 27, 1963. p. 43. Retrieved February 16, 2019 – via Newspapers.com.
- Morgan Ward at the Mathematics Genealogy Project.
- Collection Profile: Morgan Ward (1901–1963) Archived 2012-04-24 at the Wayback Machine, Caltech Library, retrieved 2010-09-12.
- Lehmer, D. H. (1993), "The mathematical work of Morgan Ward", Mathematics of Computation, 61 (203): 307–311, Bibcode:1993MaCom..61..307L, doi:10.1090/S0025-5718-1993-1182245-3.
- In Memoriam Archive MAA C. E. Hardgrove was on the faculty of Northern Illinois University from 1950 until her retirement in 1978.
- Ward, Morgan (1930), "Postulates for the inverse operations in a group", Transactions of the American Mathematical Society, 32 (3): 520–526, doi:10.1090/S0002-9947-1930-1501550-7
- Johnson, Kenneth; Vojtechovsky, Petr (2006), "Right division in groups, Dedekind-Frobenius group matrices, and Ward quasigroups", Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 75: 121–136, arXiv:math/0701716, doi:10.1007/BF02942039, S2CID 17528168