Mr Yentob, who would have been the popular choice of many of the BBC's creative and programming staff, is thought to have lost out because of a perceived lack of organisational skill.
His failure will have striking implications for the future of the corporation. The governors are known to have been impressed with Mr Yentob's belief that the BBC should abandon viewing figures as a measure of its success and reinvigorate its commitment to public service broadcasting.
He was also seen as the favourite of many in the BBC who want to see a reversal of the management reforms introduced by the current director- general, Sir John Birt.
The combination of Mr Yentob's stance on ratings and his popularity with members of staff may put him in a good position to become deputy director-general when the present deputy, Will Wyatt, retires later this year.
Tales of Mr Yentob's disorganised working style are legion at the BBC. One governor was reported yesterday as saying: "He has the greatest human presence, but it was pretty clear after his interviews that he was not going to make it. The man can't finish a sentence."
Despite having already run BBC1 and BBC2 successfully, sources say the governors balked at putting him in control of a corporation which employs 22,000 people and has a budget of pounds 2bn. "You cannot have someone in charge of a huge organisation who cannot stay focused on one idea long enough to say what's on his mind," one of the governors was reported as saying.
Those still in the race to become the next director-general are now thought to beTony Hall, the chief executive of BBC News, and Greg Dyke, the chairman of Pearson Television, whose candidacy has been overshadowed by his relationship with the Government. Mark Byford, the head of the BBC World Service, is still nominally in the running, and is known to have the backing of Sir John, but his relative inexperience and youth have made him an outside bet.
Richard Eyre, the chief executive of ITV, has been the subject of conflicting reports and may already be out of the race. He is thought to have too little experience of running a large organisation and has not spent enough time in television - he joined ITV less than two years ago from Capital Radio.
Mr Hall may benefit from those governors who are opposed to Mr Dyke because of the latter's donations to the Labour Party and close links to Tony Blair. Governors including Sir Kenneth Bloomfield and Adrian White are known to be worried that Mr Dyke could undermine the BBC's perceived political neutrality, even if they do not believe Mr Dyke himself would try to bend the BBC's line.
The selection process is running into what a senior figure described as "a meltdown" because the chairman of the governors, Sir Christopher Bland, is a strong supporter of Mr Dyke and is trying to push the other governors into accepting him.