We present parameter estimation forecasts for present and future 3D cosmic shear surveys. We demonstrate in particular that, in conjunction with results from cosmic microwave background (CMB) experiments, the properties of dark energy can be estimated with very high precision with large-scale, fully 3D weak-lensing surveys. In particular, a five-band, 10000-deg2 ground-based survey of galaxies to a median redshift of zm = 0.7 could achieve 1σ marginal statistical errors, in combination with the constraints expected from the CMB Planck Surveyor, of Δw0 = 0.108 and Δwa = 0.099. We parametrize the redshift evolution of w by w(a) = w0 + wa(1 - a) where a is the scalefactor. Such a survey is achievable with a wide-field camera on a 4-m class telescope. The error on the value of w at an intermediate pivot redshift of z = 0.368 is constrained to Δw(z = 0.368) = 0.0175. We compare and combine the 3D weak-lensing constraints with the cosmological and dark energy parameters measured from planned baryon acoustic oscillation (BAO) and supernova Type Ia experiments, and find that 3D weak lensing significantly improves the marginalized errors on w0 and wa in combination, and provides constraints on w(z) at a unique redshift through the lensing effect. A combination of 3D weak-lensing, CMB and BAO experiments could achieve Δw0 = 0.037 and Δwa = 0.099. We also show how our results can be scaled to other telescopes and survey designs. Fully 3D weak shear analysis avoids the loss of information inherent in tomographic binning, and we also show that the sensitivity to systematic errors in photometric redshift is much less. In conjunction with the fact that the physics of lensing is very soundly based, the analysis here demonstrates that deep, wide-angle 3D weak-lensing surveys are extremely promising for measuring dark energy properties.