Marsden earned his B.Sc. in Mathematics at the University of Toronto and his Ph.D. at Princeton University in 1968. Thereafter, he has worked at various universities and research institutes in the USA, Canada, the United Kingdom, France and Germany. He was one of the founders of the Fields Institute in Toronto, Canada, and directed it until 1994; at the California Institute of Technology he was the Carl F. Braun Professor of Engineering and Control & Dynamical Systems.

Marsden, together with Alan Weinstein, was one of the world leading authorities in mathematical and theoretical classical mechanics. He has laid much of the foundation for symplectic topology. He had the Marsden-Weinstein quotient named after him.

In 1981, Marsden won the Jeffery-Williams Prize. And in 1990, he received the Norbert Wiener Prize in Applied Mathematics, jointly awarded by the Society for Industrial and Applied Mathematics (SIAM) and the American Mathematical Society (AMS). Marsden was honoured "for his outstanding contributions to the study of differential equations in mechanics: he proved the existence of chaos in specific classical differential equations; his work on the momentum map, from abstract foundations to detailed applications, has had great impact." He was also awarded the Max Planck Research Award for Mathematics and Computer science in 2000. In 2005, he won the prestigious John von Neumann Lecture, which is awarded by SIAM to recognize outstanding contributions to the field of applied mathematical sciences and for their effective communication to the community. In 2006 he was elected Fellow of the Royal Society. In the same year, he also received an honorary doctorate from the University of Surrey.