I want to take away WebService call from UIViewController
I would recommend looking into MVVM architecture. You can see a simple example in this repo.
One problem with it is that its author declares and assigned view models directly in a ViewController which can be a bit problematic when writing tests. A better approach would be to inject view model so it can be easily replaced with mock. To improve that approach you can take a look at coordinators patterns, a bit more advanced example can be found here
In most cases the WebService should go in the ViewModel in the MVVM pattern. Services can be injected to ViewModels, which are responsible for managing data provided by these services. Then when they perform all logical transformations (filtering, ordering, multiplying etc.) they provide this information to a view (ViewController in our case) which just consumes it. It allows us to easily write mocks and tests. There are of course more approaches like state machine, but ViewModel as content provider and meeting point for services is most common and most universal one in my opinion.