You don't need any API or a third party tool for this. All you need to
do is to go to this official Twitter account: "Verified" and see its
"Following" list. This account follows only Verified users.!/verified/…

A minor catch here (though it may not matter for any practical purposes): Since a twitter account can't be it's own follower and the "Verified" account is a verified one, you will need to add one to the number of accounts "Verified" follows to get the actual number of verified accounts. 

As of today (Feb 28, 2012), "Verified" follows 18,589 accounts, so there are 18590 verified users.

See question on Quora