How to make custom template for search results
By using the theme function I have got it working. Here is how it looks like:

/**
 * Implements hook_theme().
 *
 * Create custom theme and template files.
 */
function mymodule_theme() {
  $themes = array(
    'my_search_result' =&gt; array(
      'variables' =&gt; array('result' =&gt; NULL, 'module' =&gt; NULL),
      'file' =&gt; 'mymodule.pages.inc',
      'template' =&gt; 'my-search-result',
    ),
    'my_search_results' =&gt; array(
      'variables' =&gt; array('results' =&gt; NULL, 'module' =&gt; NULL),
      'file' =&gt; 'mymodule.pages.inc',
      'template' =&gt; 'my-search-results',
    ),
  );
  return $themes;
}