On your iPhone, go to Settings -> Mail, Contacts, Calendars. Select ‘Add Account’ and select ‘Microsoft Exchange’. Enter your Gmail username and password when you’re asked. Now, in the ‘Server’ field, type m.google.com and select ‘Yes’ to sync contacts and calendars.
That should do it! You can also download the InTouch app on both phones, which will let you share contacts between the two.