Pls, check if DataGridComboBoxColumn xaml below would work for you:
<DataGridComboBoxColumn
SelectedValueBinding="{Binding CompanyID}"
DisplayMemberPath="Name"
SelectedValuePath="ID">
<DataGridComboBoxColumn.ElementStyle>
<Style TargetType="{x:Type ComboBox}">
<Setter Property="ItemsSource" Value="{Binding Path=DataContext.CompanyItems, RelativeSource={RelativeSource AncestorType={x:Type Window}}}" />
</Style>
</DataGridComboBoxColumn.ElementStyle>
<DataGridComboBoxColumn.EditingElementStyle>
<Style TargetType="{x:Type ComboBox}">
<Setter Property="ItemsSource" Value="{Binding Path=DataContext.CompanyItems, RelativeSource={RelativeSource AncestorType={x:Type Window}}}" />
</Style>
</DataGridComboBoxColumn.EditingElementStyle>
</DataGridComboBoxColumn>
Here you can find another solution for the problem you’re facing: Using combo boxes with the WPF DataGrid