Geospatial data and related technologies have become an increasingly important aspect of data analysis processes, with their prominent role in most of them. Serverless paradigm have become the most popular and frequently used technology within cloud computing. This paper reviews the serverless paradigm and examines how it could be leveraged for geospatial data processes by using open standards in the geospatial community. We propose a system design and architecture to handle complex geospatial data processing jobs with minimum human intervention and resource consumption using serverless technologies. In order to define and execute workflows in the system, we also propose new models for both workflow and task definitions models. Moreover, the proposed system has new Open Geospatial Consortium (OGC) Application Programming Interface (API) Processes specification-based web services to provide interoperability with other geospatial applications with the anticipation that it will be more commonly used in the future. We implemented the proposed system on one of the public cloud providers as a proof of concept and evaluated it with sample geospatial workflows and cloud architecture best practices.