You want to have the same value for Text and Tooltip?
Then you have to bind the ToolTip Property to the Text Property of your TextBlock.
<TextBlock
Name="MyTextBlock"
Text="{Binding MyProperty}"
ToolTip="{Binding ElementName=MyTextBlock, Path=Text}">
</TextBlock>
Especially for you it must be:
<TextBlock Name= "MyTextBlock"
Grid.Column="0"
VerticalAlignment="Center"
FontFamily="{DynamicResource DefaultFont}"
Foreground="{Binding HeaderTextBrush,ElementName=rndPanel}"
FontSize="15"
FontWeight="Bold"
Width="450"
ToolTip="{Binding ElementName=MyTextBlock, Path=Text}"
Text="{x:Static LibraryView:StringResources.L_AddNewLibraryWindow_SelectCompounds}"
HorizontalAlignment="Left">
</TextBlock>