After changing my website to HTTPS, the pages indexed in the Google Webmaster Tools/Search Console, have dropped 80%. Do I have to add my website again, this time with the HTTPS version?
Yes if you have added https to your website you need to add that to your Google Search Console. There you will be able to see the opposite data i.e. an increase instead of a decrease. If that doesn't happen you need to investigate further what is wrong.
To ensure you have a smooth transition from HTTP to HTTPS you need to consider few things.
Once successfully moved, make sure you got 301 redirection setup from your http version of URL to https version of URL.
Add HTTPS version of URL to Google Webmaster tools.
Load HTTPS version of xml sitemap.
Once these are done, Google may take few days to few weeks to change the indexed pages from HTTP to HTTPS version. This is also influenced by website popularity and size of the website.
Note: If above done correctly, you don't need to think too much (Number of indexed pages etc), just give the required time for the transition to take place.