James Purnell, the former Labour minister who is head of radio and education at the BBC, is to take responsibility for religion as part of his remit.
Hall said the addition to Purnell's responsibilities showed the BBC was taking "one of the big issues of our times" seriously.
The BBC recently announced that Religion and Ethics, currently based in Salford in Manchester, will soon come under the management of Factual Scotland to "simplify the existing management structure".
It was also announced that Aaqil Ahmed, head of religion and ethics at the BBC, is leaving the corporation. Ahmed lost his responsibility for commissioning programmes in 2015.
His job as head of religion and ethics will cease to exist once he leaves.
Hall is setting up an ongoing "round table" for religious leaders from January to help the BBC better reflect faith in Britain across all programming areas, not just news.
A BBC spokesman told Christian Today that Purnell will not be "head of religion" but will represent religion at the top table at the BBC. Until now there has been no one on the executive board who has been specifically responsible for religion.
He will not be involved in day-to-day commissioning but will oversee the corporation's religious "strategy", the spokesman said, working with the religious leaders on the round table.
In his speech, Hall admitted that faith in the corporation was "profoundly shaken" by the enquiry into Jimmy Saville and the revelations of how badly the BBC had let down abuse survivors.
"The last three years has been about restoring faith in the BBC, and rebuilding its foundations by securing a strong Charter. The next three years is about renewing it by delivering on a bold, ambitious vision for the future," he said, adding that the aim was to produce great public service content, for everyone.
Of the so-called "post-truth era", where presentation can override facts, he said: "But the real truth is, it has never been more important to be able to separate facts from opinion, prediction from certainty."
The BBC also played a vital role in British identity, he said.
Roger Mosey, Master of Selwyn College, Cambridge has described Purnell as a possible future director general of the BBC.