On August 1, Google’s Jade Wang announced in the Business Forum that you can now instantly verify your Google My Business listing, formerly known as Google Places and Google+ Local Listing, via Google Webmaster Tools.

Considering all the previous hassles of verifying a business in Google, we welcome this move by Google. However, you need to make sure that you’re signed in to Google My Business with the same account you’ve verified your site with Webmaster Tools. Note that not all business categories may not be eligible for instant verification. Google hasn’t either given a list of categories eligible for verification
Here if the official statement from Jade –

Good news — starting today, if you’re verifying a page for your business, you may be instantly verified on Google My Business if you’ve already verified your business’s website with Google Webmaster Tools. The verification will happen automatically, if applicable, when you attempt to verify a page for your business.
If you’d like to try instant verification, please make sure you’re signed in to Google My Business with the same account you used to verify your site with Webmaster Tools
Not all businesses with websites verified using Google Webmaster Tools will have instant verification, since not all business categories are eligible. If that’s the case, please use one of our other methods of verification (https://support.google.com/business/answer/2911778).

The process is indeed simple. Here are the steps.
Step1: You need to be signed in to Google Webmaster Tools with the same account you wish to verify your Google My Business listing.
Step 2: Open Google My Business at http://google.com/business
Step 3: Go to your unverified listing and click “Manage this page” link as shown below

Step 4: You will be directed to confirm your business as shown in the image below. Just click the check box and Continue.

Step 5: You are done. You will receive a message in your browser stating “You’ve successfully verified your Business on Google.”

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