How to add the custom button which executes a Django admin action to change form page?

You could take a look at the change_form_template and set it to a custom template of yours and override the response_change method:

class MyModelAdmin(admin.ModelAdmin):

    # A template for a customized change view:
    change_form_template="path/to/your/custom_change_form.html"

    def response_change(self, request, obj):
        opts = self.model._meta
        pk_value = obj._get_pk_val()
        preserved_filters = self.get_preserved_filters(request)

        if "_customaction" in request.POST:
            # handle the action on your obj
            redirect_url = reverse('admin:%s_%s_change' %
                               (opts.app_label, opts.model_name),
                               args=(pk_value,),
                               current_app=self.admin_site.name)
             redirect_url = add_preserved_filters({'preserved_filters': preserved_filters, 'opts': opts}, redirect_url)
             return HttpResponseRedirect(redirect_url)
        else:
             return super(MyModelAdmin, self).response_change(request, obj)

Copy the change_form.html from your site-packages/django/contrib/admin/templates/change_form.html and edit the line 40

 {% if save_on_top %}{% block submit_buttons_top %}{% submit_row %}{% endblock %}{% endif %}

to

 {% if save_on_top %}{% block submit_buttons_top %}{% custom_submit_row %}{% endblock %}{% endif %}

Also check the line:

 {% block submit_buttons_bottom %}{% submit_row %}{% endblock %}

just above the javascript block.

Then you can register a new inclusion tag somewhere in your admin.py or add it to templatetags:

@register.inclusion_tag('path/to/your/custom_submit_line.html', takes_context=True)
def custom_submit_row(context):
    """
    Displays the row of buttons for delete and save.
    """
    opts = context['opts']
    change = context['change']
    is_popup = context['is_popup']
    save_as = context['save_as']
    ctx = {
        'opts': opts,
        'show_delete_link': (
            not is_popup and context['has_delete_permission'] and
            change and context.get('show_delete', True)
        ),
        'show_save_as_new': not is_popup and change and save_as,
        'show_save_and_add_another': (
            context['has_add_permission'] and not is_popup and
            (not save_as or context['add'])
        ),
        'show_save_and_continue': not is_popup and context['has_change_permission'],
        'is_popup': is_popup,
        'show_save': True,
        'preserved_filters': context.get('preserved_filters'),
    }
    if context.get('original') is not None:
        ctx['original'] = context['original']
    return ctx

The contents of your custom_submit_line.html:

{% load i18n admin_urls %}
<div class="submit-row">
{% if show_save %}<input type="submit" value="{% trans 'Save' %}" class="default" name="_save" />{% endif %}
{% if show_delete_link %}
    {% url opts|admin_urlname:'delete' original.pk|admin_urlquote as delete_url %}
    <p class="deletelink-box"><a href="{% add_preserved_filters delete_url %}" class="deletelink">{% trans "Delete" %}</a></p>
{% endif %}
{% if show_save_as_new %}<input type="submit" value="{% trans 'Save as new' %}" name="_saveasnew" />{% endif %}
{% if show_save_and_add_another %}<input type="submit" value="{% trans 'Save and add another' %}" name="_addanother" />{% endif %}
{% if show_save_and_continue %}<input type="submit" value="{% trans 'Save and continue editing' %}" name="_continue" />{% endif %}

<input type="submit" value="{% trans 'Custom Action' %}"  name="_customaction" />

</div>

It is a lot of code, but mostly copy/paste. Hope that helps.