Measurements of Bose-Einstein correlations of π− π − pairs in central Pb+Pb collisions were performed with the NA49 detector at the CERN Super Proton Synchroton for beam energies of 20A, 30A, 40A, 80A, and 158A GeV. Correlation functions were measured in the longitudinally comoving "out-side-long" reference frame as a function of rapidity and transverse momentum in the forward hemisphere of the reaction. Radius and correlation strength parameters were obtained from fits of a Gaussian parametrization. The results show a decrease of the radius parameters with increasing transverse-momentum characteristic of strong radial flow in the pion source. No striking dependence on pion-pair rapidity or beam energy is observed. Static and dynamic properties of the pion source are obtained from simultaneous fits with a blast-wave model to radius parameters and midrapidity transverse-momentum spectra. Predictions of hydrodynamic and microscopic models of Pb+Pb collisions are discussed.