Apple Watch support requires Duo Mobile 3.8 or later. To see which version of Duo Mobile is installed on your device, go to the iOS Settings menu, then scroll down and tap Duo Mobile. The "System Info" section shows the app version.
You'll need to enable Apple Watch notifications for Duo Mobile. Open the Watch app on your phone, tap "My Watch", and scroll down then tap the entry for Duo. Enable "Show App on Apple Watch".
When you receive a push notification, you'll also see the notification on your paired Apple Watch if your phone is locked. Apple Watch’s Taptic Engine is a linear actuator inside the device that produces haptic feedback, meaning it literally taps you on the wrist whenever you receive an alert or notification. That means you’ll also feel a tap whenever a login request is sent via Duo Mobile, letting you quickly log in or deny the request.
You can approve the login or deny the login request without ever touching your phone.
You'll only see the Duo request on your watch when your phone is locked. Notifications won't go to your Apple Watch when your phone is unlocked.
You can also generate passcodes from the Duo Apple Watch app. Simply launch the app from the watch and tap an account to generate a passcode for that account.