The decision follows concerns about the concentration of media outlets in the hands of one organisation.
Rival UK media groups dismissed News Corp's offer as a "whitewash" and said they would "vigorously contest" the takeover.
News Corp, which owns the Sun, the News of the World, the Times and the Sunday Times, is looking to take over the 61% of BSkyB that it does not own.
Culture Secretary Jeremy Hunt said he intended to accept News Corp's offer rather than refer the takeover to the Competition Commission.
Ofcom, the UK media regulator, had said the deal should be referred to the commission. The European Commission has already ruled there is no reason to oppose the takeover on competition grounds.
News Corp said it welcomed Mr Hunt's decision.
It said it noted Ofcom's opinion to the culture secretary that it considered that "the revised proposed undertakings would address [its] plurality concerns".
Correspondence published today between Mr Hunt and News Corp indicates that News Corp has - under pressure - made greater concessions than it wanted to”
Opponents will have until 21 March to lodge any complaints.A number of media groups have opposed the takeover, including the Guardian, Associated Newspapers, Trinity Mirror and the Telegraph.
"We shall be vigorously contesting this whitewash of a proposal during the consultation period, as well examining all legal options," they said in a joint statement.
'More independence' Mr Hunt, responsible for deciding whether to allow the takeover, said he believed News Corp's offer to hive off Sky News would "address concerns about media plurality".
"The undertakings offered would ensure that shareholdings in Sky News would remain unchanged, and indeed offer it more independence from New Corporation than it currently has," he said.
- June 2010: News Corporation bids to take over the 61% of BSkyB it doesn't already own
- Nov 2010: Business Secretary Vince Cable asks media regulator Ofcom to look at the potential impact of the deal on media plurality
- Dec 2010: Separately, the takeover gets approval by European regulators on competition grounds
- Dec: Vince Cable stripped of powers over the deal after being recorded saying he had "declared war" on Mr Murdoch
- 13 January 2011: Media watchdog Ofcom says the bid should be referred to the Competition Commission
- 25 January 2011: Culture Secretary Jeremy Hunt recommends referral to Competition Commission, but gives News Corp time to make concessions
- 2 March 2011: BBC reports News Corp offers to spin-off Sky News
- 3 March 2011: Takeover gets government approval
Under the terms of News Corp's proposals, the board of Sky News would have a non-executive, independent chairman and a majority of non-executive, independent directors.News Corp has proposed that shares in Sky News be distributed among existing shareholders, with Mr Murdoch's company maintaining its 39% holding.
News Corp would not be allowed to increase its shareholding without the permission of the culture secretary for 10 years.
It has also offered to provide funding in the form of "a substantial revenue stream" to Sky News for 10 years.
Media analyst Steve Hewlett told the BBC the offer "rolls forward the status quo, but with an independent chairman and board".
The funding commitment and continued shareholding ensures that News Corp "has a long-term interest in Sky News prospering," he added.
BBC business editor Robert Peston said Mr Hunt's decision heralded "huge changes to the landscape of the British media industry".
A combined News Corp and BSkyB would generate revenues that would "dwarf all rivals, even the BBC", he said.
Global interests Mr Murdoch has made no secret of his desire to gain control of BSkyB.
BSkyB made a pre-tax profit of £465m in the last six months of 2010, with revenues of £3.2bn.
"BSkyB is doing very well, and News Corp considers Sky's pay-TV service as the best in the world," said Mr Hewlett.
News Corp has many interests outside the UK, including the Fox broadcast and cable networks, 20th Century Fox film studios, Harper Collins book publisher, and newspapers such as the Wall Street Journal.