これでうまくいくはずです:
<TextBlock Text="{Binding SelectedItem.Header, RelativeSource={RelativeSource AncestorType={x:Type TabControl}}}" />
これを示す完全な xaml を次に示します。
<Window x:Class="WpfApplication21.MainWindow"
xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
xmlns:local="clr-namespace:WpfApplication21"
Title="MainWindow" Height="350" Width="525">
<Window.Resources>
<ControlTemplate x:Key="TabControlControlTemplate" TargetType="{x:Type TabControl}">
<StackPanel>
<StackPanel Orientation="Horizontal">
<TextBlock Text="Selected Item header: " />
<TextBlock Text="{Binding SelectedItem.Header, RelativeSource={RelativeSource AncestorType={x:Type TabControl}}}" />
</StackPanel>
<Grid ClipToBounds="True" SnapsToDevicePixels="True" KeyboardNavigation.TabNavigation="Local">
<Grid.ColumnDefinitions>
<ColumnDefinition x:Name="ColumnDefinition0"/>
<ColumnDefinition x:Name="ColumnDefinition1" Width="0"/>
</Grid.ColumnDefinitions>
<Grid.RowDefinitions>
<RowDefinition x:Name="RowDefinition0" Height="Auto"/>
<RowDefinition x:Name="RowDefinition1" Height="*"/>
</Grid.RowDefinitions>
<TabPanel x:Name="HeaderPanel" Grid.Column="0" IsItemsHost="True" Margin="2,2,2,0" Grid.Row="0" KeyboardNavigation.TabIndex="1" Panel.ZIndex="1"/>
<Border x:Name="ContentPanel" BorderBrush="{TemplateBinding BorderBrush}" BorderThickness="{TemplateBinding BorderThickness}" Background="{TemplateBinding Background}" Grid.Column="0" KeyboardNavigation.DirectionalNavigation="Contained" Grid.Row="1" KeyboardNavigation.TabIndex="2" KeyboardNavigation.TabNavigation="Local">
<ContentPresenter x:Name="PART_SelectedContentHost" ContentTemplate="{TemplateBinding SelectedContentTemplate}" Content="{TemplateBinding SelectedContent}" ContentStringFormat="{TemplateBinding SelectedContentStringFormat}" ContentSource="SelectedContent" Margin="{TemplateBinding Padding}" SnapsToDevicePixels="{TemplateBinding SnapsToDevicePixels}"/>
</Border>
</Grid>
</StackPanel>
<ControlTemplate.Triggers>
<Trigger Property="TabStripPlacement" Value="Bottom">
<Setter Property="Grid.Row" TargetName="HeaderPanel" Value="1"/>
<Setter Property="Grid.Row" TargetName="ContentPanel" Value="0"/>
<Setter Property="Height" TargetName="RowDefinition0" Value="*"/>
<Setter Property="Height" TargetName="RowDefinition1" Value="Auto"/>
<Setter Property="Margin" TargetName="HeaderPanel" Value="2,0,2,2"/>
</Trigger>
<Trigger Property="TabStripPlacement" Value="Left">
<Setter Property="Grid.Row" TargetName="HeaderPanel" Value="0"/>
<Setter Property="Grid.Row" TargetName="ContentPanel" Value="0"/>
<Setter Property="Grid.Column" TargetName="HeaderPanel" Value="0"/>
<Setter Property="Grid.Column" TargetName="ContentPanel" Value="1"/>
<Setter Property="Width" TargetName="ColumnDefinition0" Value="Auto"/>
<Setter Property="Width" TargetName="ColumnDefinition1" Value="*"/>
<Setter Property="Height" TargetName="RowDefinition0" Value="*"/>
<Setter Property="Height" TargetName="RowDefinition1" Value="0"/>
<Setter Property="Margin" TargetName="HeaderPanel" Value="2,2,0,2"/>
</Trigger>
<Trigger Property="TabStripPlacement" Value="Right">
<Setter Property="Grid.Row" TargetName="HeaderPanel" Value="0"/>
<Setter Property="Grid.Row" TargetName="ContentPanel" Value="0"/>
<Setter Property="Grid.Column" TargetName="HeaderPanel" Value="1"/>
<Setter Property="Grid.Column" TargetName="ContentPanel" Value="0"/>
<Setter Property="Width" TargetName="ColumnDefinition0" Value="*"/>
<Setter Property="Width" TargetName="ColumnDefinition1" Value="Auto"/>
<Setter Property="Height" TargetName="RowDefinition0" Value="*"/>
<Setter Property="Height" TargetName="RowDefinition1" Value="0"/>
<Setter Property="Margin" TargetName="HeaderPanel" Value="0,2,2,2"/>
</Trigger>
<Trigger Property="IsEnabled" Value="False">
<Setter Property="Foreground" Value="{DynamicResource {x:Static SystemColors.GrayTextBrushKey}}"/>
</Trigger>
</ControlTemplate.Triggers>
</ControlTemplate>
</Window.Resources>
<TabControl Template="{DynamicResource TabControlControlTemplate}">
<TabItem Header="Tab 1" />
<TabItem Header="Tab 2" />
<TabItem Header="Tab 3" />
<TabItem Header="Tab 4" />
</TabControl>
</Window>