Ashworth joined the drinks watchdog in October 2011 following the departure of former boss David Poley.
Deputy chief executive Sarah Hanratty is covering the role until a successor is appointed.
The Portman Group was established in 1989 by the UK's leading alcohol producers. Its role was to promote responsible drinking and to help prevent alcohol misuse. In 1996, it took on the role of encouraging responsible marketing and launched its Code of Practice on the Naming, Packaging and Merchandising of Alcoholic Drinks.
The code now also covers other forms of promotion, including websites, sponsorship, branded merchandise and sampling.
Ashworth was recruited to the position of chief executive officer and president of the International Alliance for Responsible Drinking and started the job this month.
The not-for-profit organisation is dedicated to addressing the global public health issue of harmful drinking and promoting responsible drinking.
On the announcement of his departure, Ashworth said: “In the past five years, we have strengthened the UK’s self-regulatory alcohol marketing framework and challenged the industry to go further than ever before in its efforts to support central and local government in helping to reduce alcohol-related harms.
"Drinks producers and retailers have shown that they are both willing and committed partners by voluntarily removing more than 1bn units of alcohol from the market, labelling over 80% of products on shelves with key health information with 90% carrying a warning about alcohol and pregnancy, providing targeted support for local communities and funding life skills education in schools.”
The Portman Group is funded by 10 member companies that represent every sector of drinks production and collectively account for more than half the UK alcohol market.