The Charity Commission has decided not to open a formal inquiry into the Shaw Trust, but has issued the charity with advice on how to improve its governance.
The regulator began probing governance and financial management at the trust after allegations in August by Ian Charlesworth, its former chief executive.
Last week the commission announced that it had completed its investigations and had given trustees "advice and guidance regarding governance".
However, it would not reveal what advice it had given, prompting criticism from Stephen Bubb, chief executive of Acevo.
"I am astonished the commission has not published the advice it gave when there are clear implications for the sector," said Bubb. "The advice must be published in full now."
A spokeswoman for the trust, which helps disabled people find work, said the advice related to "minute-taking and clarity about our structure". She added: "Improvements on both of these fronts were already under way before the commission began its inquiry."
John Briffitt, chair of the trust, said: "We are pleased that the matter has reached a satisfactory conclusion. I hope that this will bring an end to the unhelpful and inaccurate speculation from some spectators who have sought to involve themselves in this matter without any consideration of the facts."
Charlesworth, who was dismissed in July after a disagreement with trustees over plans to expand into Australia, declined to comment on the development.