I do not think there is a specific hook for this, instead use rules and actions, simply create an action as per the code below, then go to configuration, workflow, rules and add your action to the existing rule "Update order status on full payment" or create a separate rule making sure you add a condition to check that the value order:payment-balance is <= 0.
/**
* Implements hook_rules_action_info().
*
* Add rules action to process order after payment
*/
function my_module_rules_action_info() {
$order_arg = array(
'type' => 'uc_order',
'label' => t('Order'),
);
$actions['my_module_action_process_order'] = array(
'label' => t('My Module Process Ubercart Order'),
'group' => t('My Module'),
'base' => 'my_module_action_process_order',
'parameter' => array(
'order' => $order_arg,
),
);
return $actions;
}
function my_module_action_process_order($order) {
// Do Whatever Here
}