Waddell, who was also editor of the Scottish Sun, was hailed as a big hiring for Big when he joined the company just over a year ago.
One insider told The Scotsman that he left suddenly but the company had said nothing about his departure.
The company created the new role of director of media for him and he worked on internal and external media strategy. His clients included Dart Energy which has been involved in a controversial gas drilling campaign in the Forth Valley.
After 35 years in newspapers, he said he was looking forward to bringing his experience to a new environment and described Big as the “perfect fit”.
But some media commentators wondered if he really settled into the role. He leaves after just 14 months to join a charity with offices in London and New York. He said yesterday that he would disclose more details in a few weeks time.
Alex Barr, founding director of Big, confirmed Waddell had already left the company. He said he had made a “valuable contribution” in a role created especially for him, although there were no immediate plans to find a replacement.
“I understand the unique attraction of his new role. He left with our best wishes.”
It was not known how much Waddell was paid, but it was likely to be a six-figure salary. The Scotsman revealed in March that Barr and co-founder Neil Gibson each received more than £700,000 in dividends last year.
Although directors’ pay fell, shareholders shared £1.74 million in dividends. Fellow director Zoe Ogilvie was paid £176,614, while Allan Buchan received £116,012 and Marjorie Calder £19,046. No dividends were paid the previous year.
The accounts show the Glasgow-based firm’s pre-tax profits rose 43 per cent to just over £1m in the year to 31 May as turnover edged up 4.6 per cent to £6.43m.