Westferry, Europe's largest printing plant, will remain a joint venture between Telegraph Group and Express Newspapers.
Desmond, the chairman of Express Newspapers and the chairman of Westferry, had an option to buy Telegraph Group's stake in the business after its sale to the Barclay brothers. However, he has decided not to trigger a buyout of the Telegraph's share after a meeting with Sir Frederick Barclay last week.
Desmond had fallen out with Telegraph management when, at a Westferry finance meeting, he goose-stepped around the room and ridiculed Telegraph executives for considering a sale to the German media group Axel Springer.
He also slated Black and his management team.
Black faces action after a special investigation accused him of using the Telegraph's former parent company, Hollinger, as his "personal piggy bank" for personal indulgences such as a lavish party for his wife, Barbara Amiel, and tips on shopping trips.
Westferry was used by Desmond as a pawn in his bid to buy the Telegraph titles. Under the terms of Westferry's ownership, Desmond had until 10 September to decide whether to buy out Telegraph Group. He said: "In the Barclay brothers, we have found like-minded business people with whom we can work."