SARS-CoV-2, like other coronaviruses, builds a membrane-bound replication organelle (RO) to enable RNA replication1. The SARS-CoV-2 RO is composed of double membrane vesicles (DMVs) tethered to the endoplasmic reticulum (ER) by thin membrane connectors2, but the viral proteins and the host factors involved are currently unknown. Here we identify the viral non-structural proteins (NSPs) that generate the SARS-CoV-2 RO. NSP3 and NSP4 generate the DMVs while NSP6, through oligomerization and an amphipathic helix, zippers ER membranes and establishes the connectors. The NSP6ΔSGF mutant, which arose independently in the α, β, γ, η, ι, and λ variants of SARS-CoV-2, behaves as a gain-of-function mutant with a higher ER-zippering activity. We identified three main roles for NSP6: to act as a filter in RO-ER communication allowing lipid flow but restricting access of ER luminal proteins to the DMVs, to position and organize DMV clusters, and to mediate contact with lipid droplets (LDs) via the LD-tethering complex DFCP1-Rab18. NSP6 thus acts as an organizer of DMV clusters and can provide a selective track to refurbish them with LD-derived lipids. Importantly, both properly formed NSP6 connectors and LDs are required for SARS-CoV-2 replication. Our findings, uncovering the biological activity of NSP6 of SARS-CoV-2 and of other coronaviruses, have the potential to fuel the search for broad antiviral agents.