If your list contains values and not objects you could use this code:
DataGridViewRow newRow;
foreach(var item in yourList)
{
newRow = new DataGridViewRow();
newRow.Cells[0].Value = item;
yourDataGridView.Rows.Add(newRow);
}
On the other hand if your list contains (reference type) objects you'll have to change your column to DataGridViewComboBoxColumn, then bind values from your list to comboBox control used by DataGridViewComboBoxColumn and then use code from above.
This is general approach for binding values from list to comboBox:
List<keyvaluepair><string,yourobjecttype>> listForBinding = new List<keyvaluepair><string,yourobjecttype>>();
foreach(var item in yourList)
{
listForBinding.Add(new <string,yourobjecttype>(item.ToString(),item));
}
yourDataGridViewComboBoxColumn.DisplayMember = "Key";
yourDataGridViewComboBoxColumn.ValueMember = "Value";
yourDataGridViewComboBoxColumn.DataSource = listForBinding;