The Sky broadcaster closed up 14½p – nearly 2pc – at 743p as investors gambled that telecoms regulator Ofcom could give the go-ahead for the £7.8bn transaction as early as January.
One trader said: "A couple of days ago the market was agreed the most likely succession of events would be that Ofcom referred the deal to the Competition Commission and we wouldn't hear one way or the other until September.
"Cable's comments have radically changed the views. He was seen as the major obstacle.
"Now, there's conviction that the deal will be approved, even after referral, and a significant bet, perhaps 20pc chance, that Ofcom will waive it through immediately."
Mr Cable was stripped of his responsibilities for overseeing media, telecoms and broadcasting companies after he was recorded by The Daily Telegraph boasting that he had "declared war" on News Corp chairman and chief executive Rupert Murdoch.
The Business Secretary indicated he would try to block Mr Murdoch's company from acquiring the 61pc of BSkyB that it does not already own to consolidate its business. News Corp also owns The Times, The Sunday Times, The Sun and The News of the World.
A Downing Street spokesman said: "Following comments made by Vince Cable to The Daily Telegraph, the Prime Minister has decided that he will play no further part in the decision over News Corporation's proposed takeover of BSkyB."
The powers were handed to Jeremy Hunt, the Culture Secretary, who has previously praised the efforts of Mr Murdoch for creating a third television operator.
Also on Tuesday, the European Union gave the deal unconditional regulatory approval on competition grounds. Ofcom, which is considering the impact on media plurality, is due to submit a report to the Government by December 31 about whether the deal should be referred to the Competition Commission.
One trader said: "These factors have combined to massively improve Murdoch's prospects."
