Replication of influenza viral RNA depends on at least two viral polymerases, a parental replicase and an encapsidase, and cellular factor ANP32. ANP32 comprises an LRR domain and a long C-terminal low complexity acidic region (LCAR). Here we present evidence suggesting that ANP32 is recruited to the replication complex as an electrostatic chaperone that stabilises the encapsidase moiety within apo-polymerase symmetric dimers that are distinct for influenza A and B polymerases. The ANP32 bound encapsidase, then forms the asymmetric replication complex with the replicase, which is embedded in a parental ribonucleoprotein particle (RNP). Cryo-EM structures reveal the architecture of the influenza A and B replication complexes and the likely trajectory of the nascent RNA product into the encapsidase. The cryo-EM map of the FluB replication complex shows extra density attributable to the ANP32 LCAR wrapping around and stabilising the apo-encapsidase conformation. These structures give new insight into the various mutations that adapt avian strain polymerases to use the distinct ANP32 in mammalian cells.