Since you're using form-control CSS class, I'm sure that you're using Bootstrap CSS.
In Bootstrap, it is possible to implement multi-line options using data-content attribute for select element. 
Note: For 2 first choices available below, ensure any long string value you want to show in data-content have <br /> tag inserted between them (see this example fiddle). The tag can be inserted by using String.Insert (suggested using additional property that stores wrapped value in address class):
foreach (var addr in addressAll)
{
    if (addr.address.Length >= [position_index])
    {
        // new property to store wrapped values to be displayed in data-content attribute
        addr.longAddress = addr.address.Insert([position_index], "<br />");
    }
}
1) To implement the custom attribute with asp:DropDownList server control, add it manually in code-behind after data binding. Here is the code-behind part:
protected void Page_Load(object sender, EventArgs e)
{
     List<address> addressAll = ... //get table data from SQL that has been returned as a list
     addressDdl.DataSource = addressAll;
     addressDdl.DataTextField = "address";
     addressDdl.DataValueField = "addressID";
     addressDdl.DataBind();
     addressDdl.Items.Insert(0,"--Select--");
     // before transform the list into array, use foreach loop provided above
     var arr = addressAll.ToArray();
     // note: zero-index skipped here
     for (int i = 1; i <= addressDdl.Items.Count; i++)
     {
         // add data-content attribute for select options
         addressDdl.Items[i].Attributes.Add("data-content", arr[i - 1].longAddress.ToString());
     }
}
2) As an alternative, a Repeater may be used to replace DropDownList with plain select element, but with ItemTemplate to set option attributes:
ASPX
<asp:Repeater ID="rptDeliveryAddress" runat="server">
    <HeaderTemplate>
        <select id="addressDdl">
            <option value="">--Select--</option>
    </HeaderTemplate>
    <ItemTemplate>
            <option data-content="<%# DataBinder.Eval(Container.DataItem, "[longAddress]") %>" value="<%# DataBinder.Eval(Container.DataItem, "[address]") %>"><%# DataBinder.Eval(Container.DataItem, "[address]") %></option>
    </ItemTemplate>
    <FooterTemplate>
        </select>
    </FooterTemplate>
</asp:Repeater>
3) Another way I know to use multi-line dropdown is manipulating width in CSS selector together with selectPicker:
ASPX
<asp:DropDownList ID="addressDdl" runat="server" CssClass="form-control selectpicker large-bootstrap-select" ... />
CSS
/* CSS Class */
.bs-container.large-bootstrap-select {
   .dropdown-menu {
      width: 100px; /* set this attribute with desired size in pixels */
      li a span.text {
         word-wrap: break-word;
         white-space: normal;
      }
   }
}
JS
$('#<%= addressDdl.ClientID %>').selectpicker();
References:
How to add a data-attribute to a dropdown menu with C#
Is it possible to have multi-line options?
 
        
        
` between texts. – Tetsuya Yamamoto Jul 27 '17 at 07:25