First, "EditorDefinition" is obsolete, you should use "EditorTemplateDefinition". You can bind the PropertyGridEditorColorPicker.SelectedColor to the Value of the EditorTemplateDefinition without code-behind. You only need to use the SolidColorBrushToColorConverter. Here's how to do it :
xmlns:xctk="http://schemas.xceed.com/wpf/xaml/toolkit"
<Window.Resources>
<xctk:SolidColorBrushToColorConverter x:Key="SolidColorBrushToColorConverter1" />
</Window.Resources>
<Grid>
<StackPanel>
<Ellipse x:Name="_ellipse"
Fill="Green"
Width="150"
Height="150" />
<xctk:PropertyGrid x:Name="_propertyGrid"
AutoGenerateProperties="False"
SelectedObject="{Binding ElementName=_ellipse}">
<xctk:PropertyGrid.PropertyDefinitions>
<xctk:PropertyDefinition TargetProperties="Fill" />
</xctk:PropertyGrid.PropertyDefinitions>
<xctk:PropertyGrid.EditorDefinitions>
<xctk:EditorTemplateDefinition TargetProperties="Fill">
<xctk:EditorTemplateDefinition.EditingTemplate>
<DataTemplate>
<xctk:PropertyGridEditorColorPicker SelectedColor="{Binding Value, Converter={StaticResource SolidColorBrushToColorConverter1}}"
DisplayColorAndName="True"/>
</DataTemplate>
</xctk:EditorTemplateDefinition.EditingTemplate>
</xctk:EditorTemplateDefinition>
</xctk:PropertyGrid.EditorDefinitions>
</xctk:PropertyGrid>
</StackPanel>
</Grid>