How do I bind a TabControl to a collection of ViewModels?

This isn't MVVM. You should not be creating UI elements in your view model.

You should be binding the ItemsSource of the Tab to your ObservableCollection, and that should hold models with information about the tabs that should be created.

Here are the VM and the model which represents a tab page:

public sealed class ViewModel
{
    public ObservableCollection<TabItem> Tabs {get;set;}
    public ViewModel()
    {
        Tabs = new ObservableCollection<TabItem>();
        Tabs.Add(new TabItem { Header = "One", Content = "One's content" });
        Tabs.Add(new TabItem { Header = "Two", Content = "Two's content" });
    }
}
public sealed class TabItem
{
    public string Header { get; set; }
    public string Content { get; set; }
}

And here is how the bindings look in the window:

<Window x:Class="WpfApplication12.MainWindow"
        xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
        xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
        Title="MainWindow" Height="350" Width="525">
    <Window.DataContext>
        <ViewModel
            xmlns="clr-namespace:WpfApplication12" />
    </Window.DataContext>
    <TabControl
        ItemsSource="{Binding Tabs}">
        <TabControl.ItemTemplate>
            <!-- this is the header template-->
            <DataTemplate>
                <TextBlock
                    Text="{Binding Header}" />
            </DataTemplate>
        </TabControl.ItemTemplate>
        <TabControl.ContentTemplate>
            <!-- this is the body of the TabItem template-->
            <DataTemplate>
                <TextBlock
                    Text="{Binding Content}" />
            </DataTemplate>
        </TabControl.ContentTemplate>
    </TabControl>
</Window>

^{(Note, if you want different stuff in different tabs, use DataTemplates. Either each tab's view model should be its own class, or create a custom DataTemplateSelector to pick the correct template.)}

A UserControl inside the data template:

<TabControl
    ItemsSource="{Binding Tabs}">
    <TabControl.ItemTemplate>
        <!-- this is the header template-->
        <DataTemplate>
            <TextBlock
                Text="{Binding Header}" />
        </DataTemplate>
    </TabControl.ItemTemplate>
    <TabControl.ContentTemplate>
        <!-- this is the body of the TabItem template-->
        <DataTemplate>
            <MyUserControl xmlns="clr-namespace:WpfApplication12" />
        </DataTemplate>
    </TabControl.ContentTemplate>
</TabControl>

I have a Converter to decouple the UI and ViewModel,thats the point below:

<TabControl.ContentTemplate>
    <DataTemplate>
        <ContentPresenter Content="{Binding Tab,Converter={StaticResource TabItemConverter}"/>
    </DataTemplate>
</TabControl.ContentTemplate>

The Tab is a enum in my TabItemViewModel and the TabItemConverter convert it to the real UI.

In the TabItemConverter,just get the value and Return a usercontrol you need.

In Prism you usually make the tab control a region so that you don't have to take control over the bound tab page collection.

<TabControl 
    x:Name="MainRegionHost"
    Regions:RegionManager.RegionName="MainRegion" 
    />

Now the views can be added via registering itself into the region MainRegion:

RegionManager.RegisterViewWithRegion( "MainRegion", 
    ( ) => Container.Resolve<IMyViewModel>( ).View );

And here you can see a speciality of Prism. The View is instanciated by the ViewModel. In my case I resolve the ViewModel throught a Inversion of Control container (e.g. Unity or MEF). The ViewModel gets the View injected via constructor injection and sets itself as the View's data context.

The alternative is to register the view's type into the region controller:

RegionManager.RegisterViewWithRegion( "MainRegion", typeof( MyView ) );

Using this approach allows you to create the views later during runtime, e.g. by a controller:

IRegion region = this._regionManager.Regions["MainRegion"];

object mainView = region.GetView( MainViewName );
if ( mainView == null )
{
    var view = _container.ResolveSessionRelatedView<MainView>( );
    region.Add( view, MainViewName );
}

Because you have registered the View's type, the view is placed into the correct region.