The project, which has developed an alternative economic and social model for Scotland based on policies from the Nordic countries, was originally run under the auspices of the left-wing Jimmy Reid Foundation.
But there has been growing friction between foundation director Robin McAlpine, who believes he has grown Common Weal from an idea into a movement, and the foundation's convener Bob Thomson and the late Jimmy Reid's family.
The Reid family this weekend issued a letter to directors of the company behind the foundation calling for an urgent financial review of the foundation's "far-from-transparent" finances.
The letter also referred to the family's concern about a long-standing "bitter internal dispute" and "disarray" at the foundation.
Mr McAlpine, 41, is now leaving the foundation to set up Common Weal as a standalone, non-profit enterprise, which he is expected to run. A new board is lined up, and will hold its first meeting this month. Unlike the Reid Foundation, which had no position on the referendum, the board is overwhelmingly Yes supporting.
Mr McAlpine denied he had been ejected from the foundation because of clashes, and denied the new Common Weal venture was an "ego trip" for him. He said the break was amicable and there were now talks on "transitional arrangements", such as splitting cash.