Methods, apparatus, and processor-readable storage media for automatically orchestrating deployments of software-defined storage stacks are provided herein. An example computer-implemented method includes obtaining a software-defined storage deployment request from at least one user; determining a request type associated with the software-defined storage deployment request by processing at least a portion of payload content of the software-defined storage deployment request; orchestrating one or more tasks required for carrying out the requested software-defined storage deployment based at least in part on the determined request type and the processed payload content; and performing at least one automated action based at least in part on the one or more orchestrated tasks.