We present constrained radiative transfer calculations of Lyα photons propagating through clumpy, dusty, large-scale outflows, and explore whether we can quantitatively explain the Lyα haloes that have been observed around Lyman break galaxies. We construct phenomenological models of large-scale outflows which consist of cold clumps that are in pressure equilibrium with a constant-velocity hot wind. First, we consider models in which the cold clumps are distributed symmetrically around the galaxy and in which the clumps undergo a continuous acceleration in its ‘circumgalactic’ medium (CGM). We constrain the properties of the cold clumps (radius, velocity, H i column density and number density) by matching the observed Lyα absorption strength of the CGM in the spectra of background galaxies. We then insert a Lyα source in the centre of this clumpy outflow, which consists of 105–106 clumps, and compute observable properties of the scattered Lyα photons. In these models, the scattered radiation forms haloes that are significantly more concentrated than observed. In order to simultaneously reproduce the observed Lyα absorption line strengths and the Lyα haloes, we require – preferably bipolar – outflows in which the clumps decelerate after their initial acceleration. This deceleration is predicted naturally in ‘momentum-driven’ wind models of clumpy outflows. In models that simultaneously fit the absorption and emission-line data, the predicted linear polarization is ∼30–40 per cent at a surface brightness contour of S = 10−18 erg s−1 cm−2 arcsec−2. Our work illustrates clearly that Lyα emission-line haloes around star-forming galaxies provide valuable constraints on the cold gas distribution and kinematics in their CGM, and that these constraints complement those obtained from absorption-line studies alone.