Their report has recommended sentencing statements by judges and sheriffs could be shown.
The review group, chaired by Lady Dorrian, also backed the idea of live tweeting by reporters in court.
But they said broadcasting or recording of cases involving children, sexual offences and vulnerable witnesses should not be allowed.
Lord President Lord Gill, Scotland's most senior judge, ordered the review because technology had changed dramatically in the 20 years since broadcasters were first allowed to televise some proceedings.
Three or four applications are submitted each year to film in court, but permission has rarely been given.
Lord Gill said: "I am grateful to Lady Dorrian and her group for having carried out this exercise so thoroughly.
"These well-considered recommendations have the support of the judges. I accept all of the recommendations.
"They are entirely appropriate in the contemporary world. My office will now prepare guidance on the implementation of Lady Dorrian's report."
The recommendations of the report include:
A total of 17 individuals and organisations responded to a consultation process during the preparation of the report.
The report has been welcomed by the Faculty of Advocates.
Its dean, James Wolffe QC, said: "In keeping with his vision of an open and accessible justice system - a vision which I share - the Lord President has made an important announcement about televising the courts.
"While there must be safeguards to protect the interests of justice, public understanding of the work of the courts - which is fundamental to our democracy - will be enhanced by these proposals, and I welcome them."
The Law Society of Scotland has also backed the proposals.
Fiona Robb, secretary to the Law Society of Scotland's Civil Justice Committee, said: "Used responsibly, cameras in court and the use of features like live tweeting will help to demystify the law, allowing the public to gain insight into the process and improve access to justice.
"While we have previously expressed concerns about significantly increasing the jurisdiction limit of the Court of Session and the huge impact that it is likely to have on Scotland's sheriff courts, we do believe that there will be significant improvements to the running of our courts as a result of these reforms."

The incident happened on the A923 Dundee to Coupar Angus road near Tullybaccart at about 02:30.
The 18-year-old was taken to Ninewells Hospital in Dundee but did not survive. Four other people in the car sustained minor injuries.
The road was closed for investigation work and officers are urging anyone who saw the car prior to the crash to contact them.
Diversions were in place and people travelling to the Rewind Festival in Perth were urged to allow extra time for their journey.

Jedburgh Sheriff Court heard that 67 videos were found on Mark Ross's laptop following a police raid at a house in Creel Court, St Abbs.
They predominantly featured boys aged between eight and 12.
Ross, 49, from Gateshead,  admitted possession of indecent "pseudo photographs" of children between November 2010 and December 2013.
Procurator fiscal Graham Fraser said the videos had been found after police received information that someone had been accessing images of child abuse through the internet.
The court was told that Ross was a full-time carer for his mother and his lawyer Ross Dow added that his client had been fully co-operative with the police.
Sheriff Peter Paterson said: "These are not victimless crimes.
"But I do detect a significant degree of shame about your involvement."
Ross was also given a three-year community pay back order involving work with a Northumberland sex offenders programme.
Some court cases could be shown live on television under proposals put forward by Scotland's judges.
[NEXT_CONCEPT]
A teenager has died after a one-car crash on a road north of Dundee.
[NEXT_CONCEPT]
A man found with extreme pornography on his computer has been placed on the sex offenders register for three years.