Organisers of the Museum of Free Derry had warned that the project could fall if the £1.2m grant from the Northern Ireland Tourist Board was not signed off by DETI.
It has now been revealed that the cash was approved on 31 October, but the details only emerged on Thursday.
Foyle MP Mark Durkan has welcomed the news.
He said: "I welcome DETI's approval of funding for this important project, which follows further representations made to Arlene Foster encouraging her to look positively on this application.
"Funding for the new rebuild represents a very sound investment, particularly given the Bloody Sunday Trust's outstanding work and its innovative plans for future development.
"This project will allow for a fuller appreciation of the significance of Bloody Sunday and the Saville Inquiry for the people of Derry - as well as ensure good visitor experiences of the rounded historic narrative of this city."
Part of the problem faced by the museum was that the funding, £2m in total, was coming from three different sources - the Tourist Board, lottery and Department of Social Development - and if one had failed to deliver, the whole package could have fallen.
The money will be used to fund a £2m expansion of the museum.