We combine accurate ab initio calculations of the second and third density virial coefficients, B(T) and C(T), of 4 He with measurements of its (p–ρ–T) behavior to determine the fourth density virial coefficient D(T). The measurements were made with a two-sinker, magnetic-suspension densimeter at pressures up to 38MPa. The measurements on isotherms from T=223K to T=323K were previously published; new measurements from T=323 K to T=500K are presented here. On each isotherm, a regression of the virial expansion was constrained to the ab initio values of B(T) and C(T); the regression determined D(T) as well as two apparatus-dependent parameters that compensated for systematic errors in the measurements. The percentage uncertainties of D(T) ranged from 2.6% at T=223K to 9.5% at T=400K to 24.7% at T=500K, where these uncertainties are expanded uncertainties with coverage factor of k=2 corresponding to a 95% confidence interval. These uncertainties are 1/6th of the uncertainty obtained without the ab initio values of B(T) and C(T). The apparatus-dependent parameters can be used to calibrate the densimeter, and this will reduce the uncertainty of other measurements made with this two-sinker densimeter. The new values of D(T) will find applications in accurate gas metrology, such as a primary pressure standard based on the refractive index of helium.