Deputy Prime Minister Raab said this would reinforce confidence in the justice system.
Cameras were allowed to film a criminal court case in England and Wales for the first time on Thursday, when the sentencing of a man convicted of manslaughter was broadcast live on television.
The government says the move, which was first promised a decade ago, will give the public a greater understanding of the judicial process.
Filming will be limited to the judge's sentencing remarks, and only the judge will appear on camera, with a 10-second delay for live broadcasts.
The first televised case at London's Old Bailey central criminal court saw Judge Sarah Munro jail Ben Oliver for life with a minimum jail term of more than 10 years, after he admitted in January to killing his grandfather.
Currently, hearings in London's Court of Appeal and the UK Supreme Court can be televised, and some cases in Scotland, which operates a separate judicial system, have been broadcast since 1992.
Until Thursday, cameras were strictly forbidden from criminal cases in England and Wales, with the images from hearings restricted to sketches created from memory by artists who remain banned from drawing inside the courtroom itself.
Supporters of televising sentencing hearings say it will help show the public why decisions are made, but critics fear widening this further to allow trials to be broadcast could lead to cases being sensationalised.
Some US courts allow broadcasters to film proceedings, allowing the public to watch high-profile criminal trials, and other countries such as France are considering allowing cases to be televised.
"Opening up the courtroom to cameras to film the sentencing of some the country's most serious offenders will improve transparency and reinforce confidence in the justice system," Deputy Prime Minister Dominic Raab said.
"The public will now be able to see justice handed down, helping them understand better the complex decisions judges make," he said.
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