For your requirement you will need to create Client Web Part in your SharePoint Hosted App. When you add Client Web Part in your SharePoint Hosted App solution and deploy it then you will find your App in Insert >> App Part ribbon.
You can use the default page that Client Web Part provide or else you can give path of your existing page that you already have been created in your App while adding Client Web Part.
You can find detail regarding how to create SharePoint Hosted App with Client Web Part here
If you are using SharePoint Provider Hosted App then in that case also the mechanism is same. You can add Client WebPart. You can find more detail here
Let me know whether it solves your problem or need more assist.
You can find the detail steps here which I have used in past and using it every Add-in.