At present cameras are banned from courts, apart from the Supreme Court.
The breakthrough comes after the Head of Sky News, who has spearheaded a campaign to televise court cases, wrote an open letter to the Justice Secretary Kenneth Clarke urging him to take action.
John Ryley told him the public would have better understood controversial sentences passed on those involved in recent rioting and looting if judges' remarks had been televised.
Broadcasters have been pressing for some years for cameras to be allowed into courts, but at present cameras - including video cameras - are banned from courts in England and Wales by section 41 of the Criminal Justice Act 1925.
The one exception is the Supreme Court where, for the past two years, cameras have been allowed to film proceedings.
Sky's home affairs correspondent Mark White said the changes, set to be announced by Mr Cameron on Tuesday, were a "significant development".
He said that the move would probably see broadcasters allowed to air the sentencing remarks of judges rather than entire trials.
Mr Ryley's proposal, put together with senior management at the BBC and ITN, was for limited coverage of court proceedings, which would not show vulnerable witnesses.
He said: "Sky News welcomes the decision and looks forward to working with the judiciary to bring about more transparency in our justice system."
Legal commentator Joshua Rozenberg said he was surprised that the Government was moving to change the guidelines so soon after the renewed pressure.
"You will see someone convicted, you will see someone being sentenced, but the witnesses who might otherwise be discouraged from giving evidence won't be shown under what we understand the Government's plan to be," he said.
He said the law will have to be changed in Parliament - meaning it might be up to a year before the first television pictures are aired from criminal courts.
I find it quite difficult to think of any arguments against doing it.
John Whittingdale MP
Conservative MP John Whittingdale, the chair of the Culture, Media and Sport committee, told Sky News the changes were "long overdue".
He said he would be "surprised" if any MPs or peers objected to the proposal.
"I find it quite difficult to think of any arguments against doing it.
"It seems to me fairly evident we want to encourage people to... respect the law more, this has to be the right thing to do."
However, not everyone is in favour of the changes.
Baroness Helena Kennedy, speaking earlier on Sky News, warned that such a move "undermines justice" - and that the only cases that would be given real coverage would be "salacious" ones.
In January 2010, Mr Ryley announced a campaign to get TV cameras into other courts, which he said would include legal challenges to the current ban on cameras in court.