WASP-family proteins are known to promote assembly of branched actin networks by stimulating the filament-nucleating activity of the Arp2/3 complex. Here, we show that WASP-family proteins also function as polymerases that accelerate elongation of uncapped actin filaments. When clustered on a surface, WASP-family proteins can drive branched actin networks to grow much faster than they could by direct incorporation of soluble monomers. This polymerase activity arises from the coordinated action of two regulatory sequences: (i) a WASP homology 2 (WH2) domain that binds actin, and (ii) a proline-rich sequence that binds profilin-actin complexes. In the absence of profilin, WH2 domains are sufficient to accelerate filament elongation, but in the presence of profilin, proline-rich sequences are required to support polymerase activity by (i) bringing polymerization-competent actin monomers in proximity to growing filament ends, and (ii) promoting shuttling of actin monomers from profilin-actin complexes onto nearby WH2 domains. Unoccupied WH2 domains transiently associate with free filament ends, preventing their growth and dynamically tethering the branched actin network to the WASP-family proteins that create it. Collaboration between WH2 and proline-rich sequences thus strikes a balance between filament growth and tethering. Our work expands the number of critical roles that WASP-family proteins play in the assembly of branched actin networks to at least three: (i) promoting dendritic nucleation; (ii) linking actin networks to membranes; and (iii) accelerating filament elongation.