Fill Form Data from Dropdown Selection

$("#CodeName").val($("#dropdown_id").val())

this simple line get val of dropdown and populate text field

Thank you Kamran I apologize I missed your response earlier while working on this. I am uncetain exactly where I would need to enter that, my updated php and code I have linked below since it won't let me edit my original post. I actually have two fields that I want to populate. ID=CodeName is the name of the file I'm trying to pull (which is the name from the selector) and then have the contents of that file displayed in ID=CodeValue

<input type="hidden" name="Action" value="EDIT" /><input type="hidden" name="Selection"  id="Selection" value="-1"><div>Below is the list of your saved codes. To edit your codes, select it from the list.</div>
<select size="1" name="CodeList" id="CodeList" onchange="CodeChange();"><option value="0">(Add New Code)</option>
<?php 
   $directory = $directory = 'users/' . $_SESSION['username'];
   $filesContents = Array();
   $files = scandir( $directory ) ;

   foreach( $files as $file )
 {
   if ( ! is_dir( $file ) )
 {
   $filesContents[$file] = file_get_contents($directory , $file);

  echo "<option>" . $file . "</option>";
 }
}
?>
</select>
    <h3>Saved Codes</h3>
    <form method="post" action="/evo/avsaveprocess.php">

     <input type="hidden" name="Action" value="SAVE" />
     <input type="hidden" name="CodeId" id="CodeId" value="0" />
     <table width="100%" border="0">
         <tr>
         <td>Description:</td>
         <td><input type="text" name="CodeDescription" size="40" maxlength="50" id="CodeName" value="" /></td>
          </tr>
          <tr>
          <td valign="top">Code:</td>
          <td>
            <textarea rows="10" style="width:99%" name="Code" id="CodeValue"></textarea>
               </td>
                </tr>
            </table>
            <input type="submit" value="Save" />
            </form>

Thank you Kamran, using your code I was able to get the proper jquery functionality to populate the file name into one text field, now working on figuring out how to populate the contents of that file.