The backup feature is added in a recent update which is still rolling out, hence, first of all, make sure you have the latest version of Google Drive on your iOS device.
How to Backup your iPhone or iPad’s Content on Google Drive
Once the app has been downloaded/updated, fire up Google Drive on your device and sign in with your Google account if you haven’t already. Navigate to Menu > Settings and then look for the “Backup” option. Tap that. In the new screen, you can select from “Contacts, Calendar events, Photos & Videos” which data you want to sync with Google drive. Contacts will be pushed to Google Contacts, Calendar data to Google Calendar and the rest to Google Photos. Next up, the process will commence and depending on the size of data which will vary for different phones, Google Drive will upload the content to its respective location. Do note, though, you only have a space of 15GB unless you’ve bought additionally. You can stop the backup anytime you want by hitting the blue “Stop backup” button.
That’s it, your iPhone’s content is now backed up to Google’s cloud. Unfortunately, you can’t sync messages just yet. When you power on your Android device and log in, this data will be automatically restored to the applications. Furthermore, Google has also mentioned that users should turn iMessage off before transition over to Android as it might cause difficulties in SMS deliveries. It is worth noting that Google bundles a dedicated adapter in the box if you’re purchasing a Pixel or Pixel XL, you can directly connect both phones through that. Incidentally, Apple introduced a similar app back in 2015, Move to iOS for Android for backing up contacts, calendars, photos, videos, browser bookmarks, email accounts and SMS history. You can use that in case you ever decide to return to iOS in the future.