The deep nitrogen-covered basin on Pluto, informally named Sputnik Planitia, is located very close to the longitude of Pluto's tidal axis(1) and may be an impact feature(2), by analogy with other large basins in the Solar System(3,4). Reorientation(5-7) of Sputnik Planitia arising from tidal and rotational torques can explain the basin's present-day location, but requires the feature to be a positive gravity anomaly(7), despite its negative topography. Here we argue that if Sputnik Planitia did indeed form as a result of an impact and if Pluto possesses a subsurface ocean, the required positive gravity anomaly would naturally result because of shell thinning and ocean uplift, followed by later modest nitrogen deposition. Without a subsurface ocean, a positive gravity anomaly requires an implausibly thick nitrogen layer (exceeding 40 kilometres). To prolong the lifetime of such a subsurface ocean to the present day(8) and to maintain ocean uplift, a rigid, conductive water-ice shell is required. Because nitrogen deposition is latitude-dependent(9), nitrogen loading and reorientation may have exhibited complex feedbacks(7).