Solar radio bursts are strongly affected by radio-wave scattering on density inhomogeneities, changing their observed time characteristics, sizes, and positions. The same turbulence causes angular broadening and scintillation of galactic and extragalactic compact radio sources observed through the solar atmosphere. Using large-scale simulations of radio-wave transport, the characteristics of anisotropic density turbulence from 0.1 R ⊙ to 1 au are explored. For the first time, a profile of heliospheric density fluctuations is deduced that accounts for the properties of extrasolar radio sources, solar radio bursts, and in situ density fluctuation measurements in the solar wind at 1 au. The radial profile of the spectrum-weighted mean wavenumber of density fluctuations (a quantity proportional to the scattering rate of radio waves) is found to have a broad maximum at around (4–7) R ⊙, where the slow solar wind becomes supersonic. The level of density fluctuations at the inner scale (which is consistent with the proton resonance scale) decreases with heliocentric distance as 〈δni2〉(r)≃2×107r/R⊙−1−3.7 cm−6. Due to scattering, the apparent positions of solar burst sources observed at frequencies between 0.1 and 300 MHz are computed to be essentially cospatial and to have comparable sizes, for both fundamental and harmonic emission. Anisotropic scattering is found to account for the shortest solar radio burst decay times observed, and the required wavenumber anisotropy is q ∥/q ⊥ = 0.25–0.4, depending on whether fundamental or harmonic emission is involved. The deduced radio-wave scattering rate paves the way to quantify intrinsic solar radio burst characteristics.