If patch notes are announced in an official blog, it's likely that it has an RSS or Atom feed. You can subscribe to the blog from an RSS reader and it'll appear in the feed.
And if you haven't heard of RSS readers before, welcome to the world of being able to subscribe to almost any website you want! The news and webcomics come to you, not the other way around.
Update: an example.
I open my reader (Inoreader), select "Add feed", and enter https://www.teamfortress.com/
. It detects the TF2 official blog and I select "Follow" to add it to my feeds. Now, when TF2 updates and patch notes are posted, I can refresh my reader to see the latest patch notes.