The ECG function is included in watchOS 5.1.2, according to Apple Store training documents which MacRumors obtained. The software update has been in beta testing for a few weeks, so it will likely get a full release in the near future. Apple has said the app would arrive by the end of the year.
It will only be available in regions where it has been cleared for use, because the feature is regulated. To begin with, you can only use the app if you're in the US.
The documents reportedly tell Apple Store employees to remind customers the app isn't "intended to be a diagnostic device or to replace traditional methods of diagnosis" and "should not be used to monitor or track disease state or change medication without first talking to a doctor." Additionally, they state you'll need an iPhone 5S or newer running at least iOS 12.1.1 (which is also in beta) to view your ECG data in the Health app.