You may bind to the property in the XAML of your Control:
<UserControl x:Class="MyNamespace.MyControl" ...>
<Grid>
<Label Background="{Binding SelectedBrush,
RelativeSource={RelativeSource Mode=FindAncestor, AncestorType=UserControl}}"/>
</Grid>
</UserControl>
If you set DataContext = this;
in the constructor of MyControl, you may omit the RelativeSource
of the binding:
<Label Background="{Binding SelectedBrush}"/>
Note that there is no need for the static constructor. You could write this:
public static readonly DependencyProperty SelectedBrushProperty =
DependencyProperty.Register("SelectedBrush", typeof(Brush), typeof(MyControl),
new PropertyMetadata(Brushes.AliceBlue));