As the digital age unfolds, executives face new strategic choices about how to take advantage of fast-moving technology innovations. Prior research showed that value comes not simply from adopting digital technology, but from using technology to transform the way a company does business. But while the term digital transformation is much in vogue, relatively less attention is paid to the design of the organization that must fulfill the chosen digital strategies. New digitally-enabled possibilities for designing, organizing, and managing productive work challenge leaders to make choices about how to operate (organizational design choices) as well as what to produce (strategic choices). This paper builds on interview and survey data from over 150 organizations to develop a model of digital organizational design. We identify a core set of organizational characteristics (including mindsets, practices and resources) that underpin enterprise development of Digital Capability to improve customer experience, internal operations or employee engagement. We introduce the concept of Digital Dexterity, the sustained organizational ability to rapidly adapt and self-organize to take advantage of emerging digital possibilities, and show that these same organizational characteristics are associated with digital dexterity. We argue that in a digital economy where technologies continue to improve exponentially, digital dexterity is the hallmark of a true Digital Organization. In order to build an enterprise for long term digital advantage, executives need to cultivate the unique set of characteristics of a Digital Organization that collectively enable both Digital Capability and Digital Dexterity.