No type was found that matches the controller named 'User'

In my case, the controller was defined as:

    public class DocumentAPI : ApiController
    {
    }

Changing it to the following worked!

    public class DocumentAPIController : ApiController
    {
    }

The class name has to end with Controller!

Edit: As @Corey Alix has suggested, please make sure that the controller has a public access modifier; non-public controllers are ignored by the route handler!

In my case after spending almost 30 minutes trying to fix the problem, I found what was causing it:

My route defined in WebApiConfig.cs was like this:

config.Routes.MapHttpRoute(
    name: "ControllersApi",
    routeTemplate: "{controller}/{action}"
);

and it should be like this:

config.Routes.MapHttpRoute(
    name: "ControllersApi",
     routeTemplate: "api/{controller}/{action}/{id}",
        defaults: new { id = RouteParameter.Optional }
);

as you see it was interfering with the standard route defined in RouteConfig.cs.