GlobalConfiguration.Configuration.DependencyResolver = new Ninject.Web.WebApi.NinjectDependencyResolver(kernel);
System.Web.Mvc.DependencyResolver.SetResolver(new Ninject.Web.Mvc.NinjectDependencyResolver(kernel));

private MyDependency dependency;

public MyController(MyDependency injectedDependency)
{
    this.dependency = injectedDependency;
}

private static void RegisterServices(IKernel kernel)
{
    kernel.Bind<MyDependency>().ToSelf().InSingletonScope();
}