Studies(1,2) have shown that the remnants of destroyed planets and debris-disk planetesimals can survive the volatile evolution of their host stars into white dwarfs(3,4), but few intact planetary bodies around white dwarfs have been detected(5-8). Simulations predict(9-11) that planets in Jupiter-like orbits around stars of less than or similar to 8 M-circle dot; (solar mass) avoid being destroyed by the strong tidal forces of their stellar host, but as yet, there has been no observational confirmation of such a survivor. Here we report the non-detection of a main-sequence lens star in the microlensing event MOA-2010-BLG-477Lb(12) using near-infrared observations from the Keck Observatory. We determine that this system contains a 0.53 +/- 0.11 M-circle dot white-dwarf host orbited by a 1.4 +/- 0.3 Jupiter-mass planet with a separation on the plane of the sky of 2.8 +/- 0.5 astronomical units, which implies a semi-major axis larger than this. This system is evidence that planets around white dwarfs can survive the giant and asymptotic giant phases of their host's evolution, and supports the prediction that more than half of white dwarfs have Jovian planetary companions(13). Located at approximately 2.0 kiloparsecs towards the centre of our Galaxy, it is likely to represent an analogue to the end stages of the Sun and Jupiter in our own Solar System.