For more than five decades, the shape and interactions of the heliosphere with the local interstellar medium have been discussed in the context of two competing models, posited in 1961(1): a magnetosphere-like heliotail and a more symmetric bubble shape. Although past models broadly assumed the magnetosphere-like concept, the accurate heliospheric configuration remained largely undetermined due to lack of measurements. In recent years, however, Voyagers 1 and 2 (V1 and V2) crossed the termination shock -the boundary where the solar wind drops - north and south of the ecliptic plane at 94 au(2,3) and 84 au(4) in 2004 and 2007, respectively, and discovered the reservoir of ions and electrons that constitute the heliosheath, while Cassini remotely imaged the heliosphere5 for the first time in 2003. Here we report 5.2-55 keV energetic neutral atom (ENA) global images of the heliosphere obtained with the Cassini/Ion and Neutral Camera (INCA). We compare them with 28-53 keV ions measured within the heliosheath by the low-energy charged particle (LECP) experiment onboard V1 and V2 over an 11-year period (2003-2014). We show that the heliosheath ions are the source of ENA. These observations also demonstrate that the heliosphere responds promptly, within -2-3 years, to outward propagating solar wind changes in both the nose and tail directions. These results, together with the V1 measurement of a -0.5 nT interstellar magnetic field(6) and the enhanced ratio between particle pressure and magnetic pressure in the heliosheath7, strongly suggest a diamagnetic bubble-like heliosphere with few substantial tail-like features. Our results are consistent with recent modelling(8-11).