The three broadcasters say in their letter that the change is "long overdue", and called for the new legislation to be included in the Queen's Speech in May.
Last September, the Ministry of Justice announced that it would end the courtroom filming ban that has been in place in England and Wales since 1925, but did not specify a timescale.
The letter, co-signed by BBC head of news Helen Boaden, ITN chief executive John Hardie and head of Sky News John Ryley, says that "timely progress" could be made in passing the bill into law.
"As representatives of the country's main broadcasters, we welcomed this proposal and the government's commitment to bring greater transparency to our courts," it says.
"We hope that timely progress can now be made to ensure that the Bill lifting the prohibition on cameras in court is included in the Queen's Speech in May.
"The administration of justice is a key part of a democracy. It shapes and defines a civilised society. The ability to witness justice in action, in the public gallery, is a fundamental freedom. Television will make the public gallery open to all."
Justice secretary Ken Clarke said last December that allowing cameras in courts would aid public understanding of justice, but he also insisted that trials will not become "theatrical".
This is because filming would only first be allowed for judgements in the Court of Appeal, expanding to the Crown Court "in due course". There would also not be any coverage of jurors, victims and witnesses "under any circumstances".
In the letter, the broadcasters accept that there must be "limitations" on courtroom filming, including that the presiding judge "should have complete control of what is shown from the courtroom".
They also note that even if the legislation was announced within the next few months, it would be some time before the first cases came on TV.
But the broadcasters warn that a "great deal of work" must be done by the judiciary, the court officials and the media to ensure that "the change succeeds in its chief aim of opening up courtrooms to make the judicial process more understandable and accessible".
"We recognise that concerns have been raised about the impact television coverage will have, particularly in controversial cases," says the letter.
"However, we believe that the outcome can only be positive. The experience over the last two years of live streaming from the Supreme Court has shown that the presence of cameras has not affected the course of justice in any way in this court. Instead it enhances public understanding and allows everyone to see justice being done.
"Everyone who believes in transparency should support this proposed change in the law. This is a long-overdue reform. For too long the UK has lagged behind much of the rest of the world on open justice. The time has come for us to catch up."