Use this to data bind the Source property to a URL

WebBrowserBahaviors.cs

static class WebBrowserBehaviors
{
    public static readonly DependencyProperty BindableSourceProperty =
        DependencyProperty.RegisterAttached(
            "BindableSource",
            typeof(string),
            typeof(WebBrowserBehaviors),
            new UIPropertyMetadata(null, BindableSourceChanged));

    static void BindableSourceChanged(object sender, DependencyPropertyChangedEventArgs e)
    {
        var webBrowser = sender as WebBrowser;
        if (webBrowser == null) return;

        var url = e.NewValue as string;
        if (url != null)
        {
            webBrowser.Source = new Uri(url);
        }
    }

    public static string GetBindableSource(DependencyObject obj)
    {
        return obj.GetValue(BindableSourceProperty) as string;
    }

    public static void SetBindableSource(DependencyObject obj, string value)
    {
        obj.SetValue(BindableSourceProperty, value);
    }
}

WebBrowserBahaviors.xaml

<!-- In your window XAML file, add the attched behavior-->
<WebBrowser Behaviors:WebBrowserBehaviors.BindableSource="{Binding SelectedItem.Url}" />