Driven by the rapidly changing space segment, satellite ground networks are in the midst of evolutionary change called the digital transformation. The digital transformation will enable the satellite communications (SATCOM) to realize benefits in speed of innovation, scale, and cost. More importantly, the digital transformation will help fulfill the key demands of next-generation SATCOM networks. The digital transformation comprises two components that are widely accepted and adopted in the larger telecommunications industry: digitization and virtualization. Digitization modularizes and commoditizes SATCOM modem architectures to use common hardware and introduces a new digital intermediate frequency (IF) interface. Additionally, standardization of digital IF is paving the way for these next-evolution architectures. The move to common hardware through digitization forms the basis for virtualization, which creates agile terminals that can deploy a variety of waveforms and applications. Leveraging virtualization, network function virtualization provides a new paradigm to support virtualized service chains and management of virtual network functions. Through these architectures, SATCOM-as-a-Service networks can be easily managed and deployed with custom configurations. Advanced antenna systems that support multi-band, multi-orbit, and multi-beam are also critical components of the digital transformation and are briefly explored. Through a digitally transformed ground network, SATCOM systems can leverage new operational use cases that improve network and terminal agility and resilience. In summary, we describe the key demands, technological components, and future operations of a digitally transformed SATCOM network.