You can use the power of the cloud to keep all your data in sync. In this case, using Google is best since both Android and iPhone have good support for it. Follow these steps:
On your Android device, back up your contacts to Google. The backup should happen automatically if you use your Google account on your device.
With that done, add your Google account to your iPhone.
When the account is set up, you may be able to enable contact syncing right away. If not, go to Settings -> Accounts & Passwords and tap your Gmail account.
Move the Contacts slider to the On (green) position, and the contacts you added to your Google account will sync to your iPhone.
From now on, any change you make to your iPhone address book syncs back to your Google account. You'll have a complete copy of your address book in two places and ready to transfer to other devices as needed.