The letter came from 61 former employees – and at least 45 other people who wished to remain anonymous as they “did not feel safe” – and accused the company of instilling fear, saying that being treated like a human being at the company was "sadly not a given".
The document was posted on Twitter on Wednesday night from a new account named Punks With Purpose.
It said that working at Brewdog had resulted in some staff members becoming mentally ill and that regardless of what area they worked in, there were daily “hurdles at best” and “genuine safety concerns” at worst.
A passage towards the end of the letter was directed to Mr Watt and said: “It is with you that the responsibility for this rotten culture lies.
"Your attitude and actions are at the heart of the way BrewDog is perceived, from both inside and out.
"By valuing growth, speed and action above all else, your company has achieved incredible things, but at the expense of those who delivered your dreams.”
Following the letter being posted, Mr Watt took to Twitter to share his response on Thursday morning, saying that while it was “hard to hear those comments” it would have “been harder to write them”, and they were not going to make excuses.
The apology began: “At BrewDog we are focused on building the best business we can, which is why the open letter we saw on Twitter was so upsetting, but so important.
"Our focus now is not on contradicting or contesting the details of that letter, but to listen, act and learn.”
He went on to say the company had thousands of employees who did have a positive experience of working with them, but that the letter “proves on many occasions we haven't got it right”.
It concluded: “We aren’t going to make excuses, we’re going to take action.
"From our commitment to sustainability to our passion for beer, BrewDog has always been defined by taking responsibility and continually improving.
"This is no exception”.