I want to connect a custom domain to an app built on Heroku. Can someone confirm that I actually need to buy a certificate and in addition buy the SSL addon on Heroku?
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Heroku has made it even easier to use SSL for custom domains now assuming you're not on the free tier plan (if you pay for at least one dyno you're good to go).
https://blog.heroku.com/announcing-automated-certificate-management
Basically, once you have a paid plan for your app., Heroku will generate the certs for you and any custom domains you have added. Then you need to check that you have the right forwarding setup by your domain provider etc.
To add ssl to an existing app you can run:
$ heroku certs:auto:enable -a
Then run the following command and make sure your custom domains are returned:
$heroku domains