You can transfer ownership in Google Merchant Center by adding them as an admin user. Remember that if you do so and remove yourself as a user, any website claims you made will be removed and the new owner needs to reclaim the website. This might cause all ads to get disapproved, so make sure you can do the whole change up and website claim at the same time.
Steps to undertake
Go to Google Merchant Center and click on the wrench icon in the top right corner. Then select Account access.
Click on the big blue plus button, a new screen will appear with a form. Enter the user email address.
Check the box next to admin and click on add user.
You can now remove yourself as a user by going to the wrench icon in the top right corner and select Preferences
Simply click on remove access. If the button is greyed out, that means you have not added an admin yet. So make sure to do this first.