Viruses are the only organisms known to store their genetic information solely in the form of RNA, and have thus evolved unique machinery to replicate an RNA genome and initiate viral gene expression in the infected cell. The large polymerase protein (L) of negative-strand (NS) RNA viruses is a particularly intriguing model for viral replication, where all of the enzymatic activities required for mRNA transcription, RNA modification, and genomic RNA replication are contained within a single polypeptide. Whereas the host cell requires a suite of enzymes to accomplish these tasks, L alone is the catalytic engine driving NS RNA viral replication. Here we demonstrate purification of functional L protein from Machupo virus (MACV) and reconstitute arenavirus RNA synthesis initiation and gene expression regulation in vitro using purified recombinant components. Through single-molecule electron microscopy analysis of MACV L, we provide the first structural information of viral L proteins. Comparative analysis with nonsegmented NS RNA viral L proteins reveals how the various enzymatic domains are arranged into a conserved architecture shared by both polymerases. Our in vitro RNA synthesis data defines the basis of arenavirus sequence-specific polymerase recruitment and how inter-termini interactions regulate template recognition. Moreover, we discover a new role for the arenaviral matrix protein in regulating viral RNA synthesis by locking a polymerase-template complex. The inhibitory matrix-L-RNA assembly functionally links transcription regulation and polymerase packaging, and reveals a mechanism for NS RNA viruses to ensure polymerase incorporation during virion maturation. Reconstitution of RNA synthesis in vitro establishes a new framework to understand the arenaviral polymerase complex, and our structural and biochemical experiments provide a basis for mechanistic analysis of the NS RNA viral replication machinery.