The prime minister is expected to make the announcement in his crime speech, as he pushes the agenda of greater transparency in public services. It is unclear at this stage how many courts will be televised, but ministers have already begun consulting with judges on the plan.
Cameron is likely to give the go-ahead to the televising of judicial verdicts, but it is thought this will not include the process of the trial leading up to the verdict, thus protecting witnesses from undue exposure to publicity.
Labour launched a limited trial of courtroom cameras in the court of appeal in 2004, but so far nothing concrete has materialised. Under current law, cameras - including video cameras - are banned from courts in England and Wales by section 41 of the Criminal Justice Act 1925. The only exception is the Supreme Court, where filming has been allowed for the past two years.
The allowance of TV cameras in courts has always been held back in the UK by the prospect of high profile trials descending into media circuses, such as the OJ Simpson trial in the US.
But Downing Street officials believe the increased transparency would help the public understand the court process, particularly in the aftermath of the UK riots.
Keir Starmer, the director of public prosecutions, said in May that he would support the idea of allowing TV cameras in court rooms, but there must be "appropriate safeguards" in place.
"In principle I would support a proposal that judgments, judges' closing remarks and judicial sentencing in criminal cases could be televised," he told a Society of Editors meeting
"Therefore there would need to be appropriate safeguards, particularly in cases involving vulnerable individuals, and any requests to televise any part of the court process should be subject to the judge's individual discretion."
John Ryley, the head of Sky News, has long called for TV cameras to be allowed in courtrooms to help tackle the "growing public dissatisfaction with the judicial process".
Ryley wrote an open letter to justice secretary Ken Clarke last month outlining a proposal, put together with senior management at the BBC and ITN, for limited coverage of court proceedings, without showing vulnerable witnesses.
Discussing Cameron's expected move today, Ryley said: "Sky News welcomes the decision and looks forward to working with the judiciary to bring about more transparency in our justice system."
Conservative MP John Whittingdale, the chair of the Culture, Media and Sport select committee, told Sky News that the changes were "long overdue". He also said that he would be "surprised" if any MPs, or peers in the House of Lords objected to the proposal.
"I find it quite difficult to think of any arguments against doing it," Whittingdale said.
"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, the proposal has not received universal support, as Baroness Helena Kennedy told Sky News that such a move "undermines justice", because the only cases likely to be given TV coverage would be the "salacious" ones.