WPF

<Window x:Class="SimpleWpfTabTest.Window1"
  xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
  xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
  Title="Window1" Height="300" Width="300">
  <Grid>
  <Grid.RowDefinitions>
    <RowDefinition Height="Auto"/>
    <RowDefinition Height="20" />
  </Grid.RowDefinitions>
  <TabControl Name="myTab" Grid.Row="0">
  </TabControl>
  <Button Name="btnAddTab" Grid.Row="1" Click="btnAddTab_Click" />
  </Grid>
</Window>

private void btnAddTab_Click(object sender, RoutedEventArgs e)
{
  // Create a TabItem
  TabItem child = new TabItem{Name="childTab" + myTab.Items.Count.ToString(), Header="Added"};
  // The TabItem needs a content holder - I'm using a StackPanel
  StackPanel childPanel = new StackPanel();
  child.Content = childPanel;
  // The button will be added as a child of the stack panel.
  Button myButton = new Button { Name = "hello", Content = "Woopee" };
  childPanel.Children.Add(myButton);
  // Add the TabItem to the tab
  myTab.Items.Add(child);
  // And set the focus to it.
  child.Focus();
}

<Window x:Class="AddTabItem.Window1"
    xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
    xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
    Title="Window1" Height="300" Width="300">
    <Grid>
     <Grid.RowDefinitions>
         <RowDefinition Height="*" />
         <RowDefinition Height="25" />
     </Grid.RowDefinitions>
     <TabControl x:Name="TabControl1" 
                 VerticalAlignment="Stretch" HorizontalAlignment="Stretch"
                 Grid.Column="0" Grid.Row="0" Grid.RowSpan="1" />
        <Button x:Name="btnAddTab" Content="Add Tab" Click="btnAddTab_Click"
                Grid.Row="1" Grid.RowSpan="1"/>
     </Grid>
</Window>

namespace AddTabItem
{
    /// <summary>
    /// Interaction logic for Window1.xaml
    /// </summary>
    public partial class Window1 : Window
    {
        public Window1()
        {
            InitializeComponent();
        }

        private void btnAddTab_Click(object sender, RoutedEventArgs e)
        {
            AddTabs();
        }

        private void AddTabs()
        {
            TabItem tabitem = new TabItem();
            Button button = new Button();
            button.Content = "Added Button!";
            tabitem.Content = button;
            TabControl1.Items.Add(tabitem);
            TabControl1.SelectedIndex = TabControl1.Items.Count;
        }
    }
}