Microsoft has confirmed that "Project Spartan", the code name for their next-generation web browser, will be included in the next preview build of Windows 10. That build should be released to members of the Fast update ring sometime in April.
The upcoming release of Project Spartan was announced on Microsoft's Internet Explorer blog, which also covered the new features and improvements the IE team has made to the browser rendering engine in the newly launched 10041 build of Windows 10. You can check out the highly technical details in the blog post.
Project Spartan will use that new rendering engine along with a new user interface and support for extensions, similar to Google's Chrome browser. Project Spartan will be the only web browser available for Windows 10 on smartphones, but a version of IE 11 will be available for PCs as well for legacy website support.
For those using the 10041 build of the Windows 10 preview, you can enable the EdgeHTML engine powering "Project Spartan" now and use it in Internet Explorer.