The government has said it is "minded to accept" News Corp's assurances about the spin-off of Sky News, but is to consult on some fresh conditions.
The spin-off of Sky News is the key condition if News Corp is to be allowed to take full ownership of BSkyB.
The conditions include having an independent editorial director at Sky News board meetings and for Sky News to continue to be promoted on other Sky channels.
The consultation will run until 8 July.
After that date, the Secretary of State for Culture, Olympics, Media and Sport, Jeremy Hunt, will take a final decision on whether to allow the takeover or refer it to the Competition Commission.
Earlier advice from the Office of Fair Trading and media regulator Ofcom expressed concern about News Corp owning too much of the British media.
Last June, News Corp offered 700 pence a share for BSkyB, but the board of BSkyB told it to come back with a higher offer.
Since then, BSkyB shares have risen significantly, and closed at 846.5p on Thursday.
Even if the takeover is cleared by the culture secretary next week, the deal could still stumble if a price cannot be agreed.
The company currently holds a 39% stake in BSkyB and owns the Sun and Times newspapers.
News Corp offered to spin off Sky News as an independent company, but continue to fund it, in order to prevent the takeover deal being referred to the Competition Commission.
Mr Hunt launched a consultation on the plans on 3 March, as a result of which he has added four extra conditions to the deal:
- Sky News board meetings will be attended by an independent director with editorial experience when editorial decisions are to be made
- A monitoring trustee will be appointed to make sure News Corp applies with its undertakings on Sky News
- Other Sky channels will continue to promote Sky News
- Sky News' Articles of Association have to be approved by the secretary of state
The government received more than 40,000 representations in its consultation, but said there was nothing to change its earlier view that the spin-off of Sky News would make the BSkyB takeover acceptable.
The deal has been vigorously opposed by an alliance of other newspapers, including the publishers of the Guardian, the Daily Mail and the Daily Telegraph.
Mr Hunt was called to the House of Commons to answer an emergency question about BSkyB from Labour MP Tom Watson.
"I'm sure the secretary of state will get his reward for this decision but he will pay a very high political price," Mr Watson said.
"This shady deal would shame a banana republic."
Mr Hunt responded by stressing that he had taken independent advice on the issue.
"I am perfectly well aware that on an issue like this, no-one is going to trust the motives of politicians," he said.
"That is why, at every stage, I have sought independent advice from Ofcom, the independent regulator, and from the Office of Fair Trading."
BBC business editor Robert Peston said the ruling meant that the culture secretary accepted that some of the critics of the deal were right, but that the criticisms were not enough for him to feel that he wants to block the takeover.
"He is, he thinks, taking steps to allay the concerns that Sky News will simply become another identikit voice within the News Corp stable rather than maintaining the kind of independence that it's had over many years," he said.