Google already sends email notifications when a new device accesses your account, but people are programmed to ignore email. According to Google, native Android notifications are four times more effective at getting your attention, so that's what it's going to show you from now on when devices are added to your account.
The new notification will ask, "Did you just sign in?" If the answer is yes, you can just dismiss the notification. If not, tap the "Review account activity" button to check out the details of the new device. This gives you the opportunity to change your password or add two-factor authorization if you're worried someone else has accessed your account.
This feature is rolling out to all users, presumably via Google Play Services. You can expect it to be live in a week or two at most.