Broadcasters will be allowed to screen footage of judgments in England and Wales for the first time as part of "unprecedented plans to improve transparency", Mr Clarke said.
But critics warned the move risked turning justice into a reality show, providing a platform for "eccentric" legal professionals and creating theatre akin to US TV show Judge Judy.
It will be the first time that cameras have been allowed in courts other than the Supreme Court since filming was banned by the Criminal Justice Act 1925.
Mr Clarke said he wanted to remove the ban "as soon as parliamentary time allows" so cameras could be used to film judgments first in the Court of Appeal and then in the crown courts.
Only judges' remarks will be shown - not those of victims, witnesses, offenders or jurors.
A consultation process involving the Lord Chief Justice Lord Judge will now take place to ensure the move "does not hinder the administration of justice and that it protects victims, witnesses, offenders and jurors", he said.
"But I am clear that this must not give offenders opportunities for theatrical public display," he added.
But Tory MP Roger Gale said it risked turning justice into a reality show and providing a platform for "eccentric" legal professionals.
Mr Gale, a former TV producer, said screening Parliament had resulted in grandstanding by MPs and a concentration on "juicy" extracts at the expense of less entertaining debates.
"I believe that the televising of the closing speeches in law courts and the passing of sentences will create the same effect as thrusting barristers seek to impress the media with fee-improving performances and the more eccentric members of the judiciary use the TV platform to address the nation," he said.
"The courts are supposed to be a place where justice is done and where it is, by those actually present and listening to the evidence, seen to be done. That must not be allowed to change.
"This is not about transparency or democracy, it is about television showbusiness and we do not need our law courts to be turned into yet another reality TV show."
Javed Khan, chief executive of Victim Support, also warned against allowing the filming of court cases to become "a form of reality entertainment like Judge Judy".
While the move to make sentencing decisions more transparent was welcome, he said, proper safeguards are needed "to protect victims and witnesses from the added stress of cameras in court".
Broadcasters have been pressing for a law change for a number of years, but the only exception to the ban has been the Supreme Court, where cameras have been allowed to film proceedings for the past two years.
John Ryley, head of Sky News, which has been campaigning for cameras in court, wrote an open letter to Mr Clarke last week calling for proceedings to be televised.
The public would have better understood controversial sentences passed on those convicted after the riots if judges' remarks had been televised, he said.
Earlier this year, Director of Public Prosecutions Keir Starmer QC revealed he was also in favour of the idea, saying it would allow the public to "see justice".
A consortium of broadcasters was allowed to film appellate courts and prepare dummy programmes in an experimental run in 2004-05. The then Lord Chancellor, Lord Falconer, was said in November 2006 to be in favour of allowing cameras to film criminal and civil trials.
Max Hill QC, chairman of the Criminal Bar Association, added that barristers had nothing to fear from increased public scrutiny, but warned that just showing extracts of the trial process could create a misleading impression.
Peter Lodder QC, chairman of the Bar Council, added that any broadcasts "must be in the public interest and in the interests of justice".
And shadow justice secretary Sadiq Khan warned that it would be "extremely important to ensure that careful controls are in place to protect jurors, victims and witnesses, particularly in complex and high-profile cases".
There are no detailed timings for the move, but it is understood that legislation to remove the ban on cameras in courts is unlikely this year.
Mr Clarke also announced plans to publish "an unprecedented level of information about the performance of courts" in an attempt to enable members of the public to see how their local courts are working.
This will include court-by-court statistics for the time taken for cases to be processed, from offence to conviction; details on how many trials were ineffective and why they were ineffective; and anonymised data on each case heard at local courts and the sentences given.
Details of how many people have been convicted or released from prisons in each area and how often they re-offended afterwards will also be published.
PA
