Newly transcribed eukaryotic precursor messenger RNAs (pre-mRNAs) are processed at their 3′ ends by the ~1-megadalton multiprotein cleavage and polyadenylation factor (CPF). CPF cleaves pre-mRNAs, adds a polyadenylate tail, and triggers transcription termination, but it is unclear how its various enzymes are coordinated and assembled. Here, we show that the nuclease, polymerase, and phosphatase activities of yeast CPF are organized into three modules. Using electron cryomicroscopy, we determined a 3.5-angstrom-resolution structure of the ~200-kilodalton polymerase module. This revealed four β propellers, in an assembly markedly similar to those of other protein complexes that bind nucleic acid. Combined with in vitro reconstitution experiments, our data show that the polymerase module brings together factors required for specific and efficient polyadenylation, to help coordinate mRNA 3′-end processing.