Google Photos has made transferring your photos from the Google Photos app to an iPhone or iPad very straightforward.
Open the Google Photos app on your iPhone. Select all your photos by dragging your finger across them and click the share icon in the menu. Choose Save to Device and your photos will begin downloading to the Camera Roll of your iPhone’s Photos app.
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Below is a step-by-step walkthrough of the process. Before you begin ensure you have enough storage to complete the transfer and, if you are connected to the internet via mobile cellular data rather than WIFI, be sure you have sufficient data allowance.
If you don’t have the Google Photos app installed on your iPhone, start by downloading the app from the Apple App Store.

Once downloaded you’ll need to sign in to the app using your Google account.

You’ll then need to select all your photos by dragging your finger across and down the page, making sure each photo has a blue tick in the corner.

Having selected everything, press the Share icon from the menu bar, in the top, right corner of the screen.

Choose 'Save To Device' to initiate the transfer process.

Be patient, because, depending on how many photos and videos you have to download, the process may take some time.

You will receive a notification once the transfer is complete and, if you open your Apple Photos app, you should see a copy of all your photos.

Syncing your iphone with Google Photos is a great free way of backing up your photos automatically, without really having to think about it.
As a general rule, your iPhone will automatically sync with Google Photos by default. You can check that sync is enabled by going into your Google Photos settings, and ensuring Backup and Sync is turned on.