The Milky Way galaxy has several components, such as the bulge, disk and halo. Unravelling the assembly history of these stellar populations is often restricted because of difficulties in measuring accurate ages for low-mass, hydrogen-burning stars. Unlike these progenitors, white dwarf stars, the 'cinders' of stellar evolution, are remarkably simple objects and their fundamental properties can be measured with little ambiguity. Here I report observations of newly formed white dwarf stars in the halo of the Milky Way, and a separate analysis of archival data in the well studied 12.5-billion-year-old globular cluster Messier 4. I measure the mass distribution of the remnant stars and invert the stellar evolution process to develop a mathematical relation that links this final stellar mass to the mass of their immediate progenitors, and therefore to the age of the parent population. By applying this technique to a small sample of four nearby and kinematically confirmed halo white dwarf stars, I calculate the age of local field halo stars to be 11.4 ± 0.7 billion years. The oldest globular clusters formed 13.5 billion years ago. Future observations of newly formed white dwarf stars in the halo could be used to reduce the uncertainty, and to probe relative differences between the formation times of the youngest globular clusters and the inner halo.