In a new mission statement sent to Microsoft employees, posted online by Geekwire, Nadella said gaming will be key in realising a "broader vision for Windows," as the company seeks to unite all its gaming-oriented initiatives.
"We will pursue our gaming ambition as part of this broader vision for Windows and increase its appeal to consumers," he said.
"We will bring together Xbox Live and our first-party gaming efforts across PC, console, mobile and new categories like HoloLens into one integrated play."
Nadella also said Microsoft will aim to deliver experiences centered on the mobility that is enabled by the cloud.
"We will build the best instantiation of this vision through our Windows device platform and our devices, which will serve to delight our customers, increase distribution of our services, drive gross margin, enable fundamentally new product categories, and generate opportunity for the Windows ecosystem more broadly."
Microsoft named Nadella as its chief executive in February 2014, following the departure of Steve Ballmer. When announcing his appointment, Microsoft highlighted Nadella's work in establishing the cloud infrastructure behind Xbox, as well as Bing and Office.
In January 2015, Xbox head Phil Spencer announced that Windows 10 will support Xbox One game streaming, allowing games to be played on PCs and tablets running the latest version of Microsoft's operating system.
"We have to put the gamer at the centre of every experience," Spencer said at the time.
Days before E3 2015, VR giant Oculus revealed its Rift device will include the Xbox One controller, and Xbox One owners will be able to stream their games to the Rift.