Solution:
 1. XAML:
<DataGrid x:Name="DataGrid" AutoGenerateColumns="False" CanUserAddRows="True">
        <DataGrid.Columns>
            <DataGridTextColumn     Header="User UName" Width="Auto" Binding="{Binding UName}"/>
            <DataGridComboBoxColumn x:Name="ComboBoxColumn" Header="Country" Width="Auto" DisplayMemberPath="name" SelectedItemBinding="{Binding CountryData}"/>
        </DataGrid.Columns>
    </DataGrid>
2. Code behind:
public partial class MainWindow : Window
{
    public MainWindow()
    {
        InitializeComponent();
        InitData();
        ComboBoxColumn.ItemsSource = CountriesCollection;
        DataGrid.ItemsSource = UsersCollection;
    }
    private void InitData()
    {
        UsersCollection = new ObservableCollection<UserData>(new List<UserData>
        {
            new UserData
            {
                UName = "Greg",
            },
            new UserData
            {
                UName = "Joe",
            },
             new UserData
            {
                UName = "Iv",
            }
        });
        CountriesCollection = new ObservableCollection<Country>(new List<Country>
        {
            new Country("Ger", "1500"),
            new Country("Fra", "1500"),
            new Country("Ru", "1500"),
            new Country("Bel", "1500"),
        });
    }
    public ObservableCollection<Country> CountriesCollection { get; set; }
    public ObservableCollection<UserData> UsersCollection { get; set; }
}
3. User model:
 public class UserData
{
    public string UName { get; set; }
    public object CountryData { get; set; }
}
4. tool tip support: replace a desired combo box column with next xaml code:
 <DataGridComboBoxColumn x:Name="ComboBoxColumn" Header="Country" DisplayMemberPath="CountryName"
                                    ItemsSource="{StaticResource CountriesArray}" Width="Auto"
                                    SelectedItemBinding="{Binding CountryData, UpdateSourceTrigger=PropertyChanged}">
                <DataGridComboBoxColumn.CellStyle>
                    <Style TargetType="DataGridCell">
                        <Setter Property="ToolTip">
                            <Setter.Value>
                                <ContentControl Content="{Binding }">
                                    <ContentControl.ContentTemplate>
                                        <DataTemplate DataType="{x:Type soDataGridProjectsHelpAttempt:UserData}">
                                            <DataTemplate.Resources>
                                                <system:String x:Key="NoAnyEntriesKey">
                                                    No any entry presented
                                                </system:String>
                                            </DataTemplate.Resources>
                                            <TextBlock Text="{Binding CountryData.Description, FallbackValue={StaticResource NoAnyEntriesKey}}"></TextBlock>
                                        </DataTemplate>
                                    </ContentControl.ContentTemplate>
                                </ContentControl>
                            </Setter.Value>
                        </Setter>
                    </Style>
                </DataGridComboBoxColumn.CellStyle>
            </DataGridComboBoxColumn>
and take in account you nedd to extend Country model with description property.
regards,