Christodoulou was born in Athens and received his doctorate in physics from Princeton University in 1971 under the direction of John Archibald Wheeler.

In the period 1987–1999 he published a series of papers on the gravitational collapse of a spherically symmetric self-gravitating scalar field and the formation of black holes and associated spacetime singularities.

Namely, that a sufficiently strong flux of incoming gravitational waves leads to the formation of a black hole.

In 2019 he published a book[13] which addresses the development of shocks past the point of formation by studying a free boundary problem with singular initial conditions.

[15] In 2011, he and Richard S. Hamilton won the Shaw Prize in the Mathematical Sciences,[16] "for their highly innovative works on nonlinear partial differential equations in Lorentzian and Riemannian geometry and their applications to general relativity and topology".