Based on my understanding of this page at China National Tourism Administration, there are currently 125 countries with Approved Destination Status. Google translates the page as “Outbound travel destination country where area business has been officially launched”, and the dates and countries agree with this paper from University of Hawaii (linked in Henning’s comment on the question). Since 2012 a few countries has been added. Below is the complete list of countries with Approved Destination Status as of August 8th, 2017, with the year the countries were added.
Starred countries are countries I’ve added based on my translation of the page of China National Tourism Administration, linked above. I’ve included the picture on that page below, feel free to improve my translations.
Credit:stackoverflow.com‘