It appears that although Valve partnered with HTC to create the HTC Vive, they have a completely different agenda when it comes to its Steam platform. Valve are actively prompting users of the Oculus Rift to install SteamVR, which is Valve’s solution to bring the Steam gaming experience to virtual reality.
Valve revealed in early 2015 that it was partnering with HTC and it seemed that the HTC Vive would have exclusive access to the Steam platform through the service, making it a very attractive marketing opportunity to push sales of the Vive. However, Valve have made it clear that it sees SteamVR as an agnostic service, and aims to not only bring SteamVR to the Oculus Rift, but quite possibly a wide range of VR headsets.
Among the latest updates to a service that has worked ever since the DK2 development headset, Steam itself now prompts a user to install SteamVR when it detects an Oculus Rift plugged into a PC. SteamVR is an optimized version of Steam created specially for use on VR headsets within a virtual reality environment and allows a user to have the same functionality as its desktop counterpart. Buying games, browsing content, and interacting with friends is all included in SteamVR, while optimized for virtual reality.
You can follow these instructions to get your Rift working with SteamVR.