New: (posted September 2016)
You can connect a verified Maps listing to an existing Google+ account by following this process:
Google Top Contributor Kamal Tailor has provided most of the information you see here. And to start, he says “there is no merge process for pages, or profiles.”
Some people have called it this, but Kamal says it is a misunderstanding of the process.
You can, however ‘convert’ a Google Local Page to a Brand Page, or vice versa.
But Google Top Contributor Peggy K says it is more like a “feature swap: you have a verified Local Page and a Brand Page. This process moves the Local features to the Brand Page, and in the process the original Local Page becomes a Brand page.”
Recommendation - get advice before you do this yourself, just to be 100% sure, especially if you have a lot of followers on a page!
Let’s say you have a verified Google+ Local Page
You will need to create a new brand page.
Then needs to use that new brand page in the conversion process.
This brand page will become the verified Local page.
The original Verified local page will become the brand page.
To create a new page, go here: plus.google.com/pages/create and ‘select the brand category’.
To find this:
Go to the ‘left side menu’
Look at the ‘Top right’
Click on ‘Get Your Page’
Via the My Business app, it is:
Open the app, and then
Tap the menu/3dots/gear button,
Select create page
Choose the appropriate options for your business, and then use a different profile image so you can differentiate between your two pages.
What is ‘the conversion’ process?
And then choose "I've already created a page for my business"
More useful information from Mike Blumenthal here too.