Zac Hall, writing for 9to5Mac on Apple’s first Android app to move user data to iOS:

Once you complete the selection process, the app creates a private Wi-Fi network used by both devices to wirelessly transfer content. After the transfer process is complete, Move to iOS will notify you if any content was not able to move to your new iPhone or iPad, then recommend recycling your old Android phone at a local Apple Store. After continuing the setup process on the iPhone or iPad, the settings and content should appear intact.

The process is integrated with iOS 9’s new setup flow – you get an option to import data from Android when setting up an iOS 9 device for the first time. The Android app is available here (and it’s got some…interesting customer reviews.)