Hunt said that News Corp's proposal to spin off Sky News as an independently-listed company should go ahead as a way to allay media plurality concerns about the takeover.
The culture secretary provisionally approved the move on March 3, but asked Ofcom and the Office of Fair Trading (OFT) to examine the proposal, which he said has resulted in a "more robust set of undertakings" being put forward.
The extra measures include a requirement for Sky News board meetings to include an independent director with senior journalism experience to oversee editorial decisions. A monitoring trustee would also be appointed to ensure News Corp complies with the rules of the undertakings in the run-up to the spinoff.
Sky must continue to cross promote Sky News across its channels and the Sky News' articles of association must be approved by the sitting culture secretary.
A further seven-day consultation on the revised undertakings will now run until July 8, enabling any final objections to be submitted.
"I am aware of the huge interest in the proposed merger and am grateful to those who responded to the consultation. I have considered carefully the points raised and, as at all steps in this process, taken advice from the independent regulators," said Hunt.
"The regulators have confirmed that the proposed undertakings are still sufficient to ensure media plurality. I could have decided to accept the original undertakings but a number of suggestions were made in response to the consultation which could further strengthen the undertakings, particularly around editorial independence, business viability and the articles of association. I am therefore proposing some changes to the undertakings and I will now hold a further public consultation."
More than 40,000 submissions were received by the government in Hunt's consultation on the Sky News plan, backed up by an almost identical number on internet campaigns.
Hunt also met with representatives from Trinity Mirror, the Guardian Media Group, the Telegraph Media Group, Associated News and Media, law firm Slaughter and May and campaign group Avaaz to discuss media plurality concerns about the takeover.
Under the News Corp plan, the loss-making Sky News would be "spun off" as a new publicly-listed company called Newco, with independent funding guaranteed for the next ten years.
News Corp will licence the Sky News brand to the operation for seven years, offering an incentive for the company to pitch for a second funding deal. Murdoch will retain a 39.1% stake in Newco, with the remaining shares held by existing shareholders in Sky.
To ensure editorial independence and integrity for Sky News, the company would have a board made up of independent directors, including an independent chair, as well as a corporate governance and editorial committee.
Hunt's approval for the plan, barring any final hurdles, will trigger a round of frantic price negotiations between News Corp and Sky's independent directors.
On Monday, it was reported that Crispin Odey, one of Sky's biggest investors, claimed that the pay-TV giant is worth £19bn, meaning News Corp would have to pay an eye-watering £11.6bn for the 61% of shares that it does not already own.