Three main options for transferring contacts:
More useful tips for smartphone users can be found here .
There is an official Move to iOS application from Apple in the Play Store just for these purposes, or manually. All methods are described here: How to transfer contacts and other data from Android to iPhone.
To do this, you need to export contacts to a special file through the phone book on the Andriod device (select export to a USB flash drive or internal storage). Then send this file to your mail and log into it from the iPhone. Open the file and the phone itself will offer to create new contacts.