Gmail will help you out to shift your contacts, you need to keep you pace in Settings, Accounts and then Google, after that step ahead to Sync Contacts. Following these steps will make you see the sync between your contacts and Gmail address book account. After that step forward to Settings, Mail, Contacts, Contacts and Calendars and to Add Account on the iPhone. Now after selecting Google, sign-in using the Google account with which you’ve synced your phone contacts. Before sync, make sure you’ve ‘Contacts’ enabled in the setting.