They had urged a judge in London to grant an order which would force BT to cut off or impede customers' access to a website accused of "flagrant" copyright infringement.
Mr Justice Arnold, giving his reserved ruling in the case following a hearing last month, announced: "I will make an order substantially in the form sought by the studios."
Major studios, including Twentieth Century Fox, Paramount Pictures Corporation and Disney Enterprises brought the proceedings over the Newzbin2 website, which has around 700,000 members.
The action, brought on behalf of all members of the Motion Picture Association of America, is believed to be the first in Britain where an attempt is being made to force an internet provider to block a site under the 1988 Copyright, Design and Patents Act (CDPA).
Film-makers told the court they wanted BT to block Newzbin with the same system that stops access to sites hosting child sex abuse images.
Richard Spearman QC, arguing for an injunction on behalf of the applicants at the recent hearing, told the judge that the Newzbin copyright infringement was being carried out on a "grand scale".
The general economic impact of piracy on the film and TV industry was, he said, "nothing short of staggering".
He told the court: "If the order is not made, websites such as Newzbin will simply be able to move offshore, anonymise the individuals behind the website and cock a snook at the courts and at rights holders who put their trust in the courts."
BT contested the claim for an injunction, arguing that there is no jurisdiction for the court to make the order sought against it under the CDPA.
In written argument before the court, submitting that the injunction application should be dismissed, Antony White QC, for BT, argued that if the court ordered it to block access to the Newzbin2 website "there would be nothing to stop countless other claimants coming forward demanding that BT block other websites alleged to contain unlawful material".
After today's ruling Bt said in a statement: "This is a helpful judgment, which provides clarity on this complex issue.
"It clearly shows that rights holders need to prove their claims and convince a judge to make a court order.
"BT has consistently said that rights holders need to take this route.
"We will return to court after the summer to explain what kind of order we believe is appropriate."
Mr Justice Arnold said he was making an order that had been agreed between the parties pending a further hearing in October when the "precise wording" of the order would be dealt with.
Lord Puttnam, president of the Film Distributors' Association, said: "Today's result is an important victory in the battle against a commercial pirate site which refused to operate within the law.
"Finally, it seems we have a way to deal with rogue sites which will benefit the film industry, including UK independent distributors and, more broadly, the entire creative sector."
Chris Marcich, the Motion Picture Association's European president, said: "This ruling from Mr Justice Arnold is a victory for millions of people working in the UK creative industries and demonstrates that the law of the land must apply online.
"This court action was never an attack on ISPs but we do need their cooperation to deal with the Newzbin site which continually tries to evade the law and judicial sanction.
"Newzbin is a notorious pirate website which makes hundreds of thousands of copyrighted products available without permission and with no regard for the law."
Spyro Markesinis, vice-president (business and legal affairs), of Momentum Pictures, said: "Without licensing revenues, films simply cannot be funded or produced.
"If that means a film like The King's Speech may not be made in the future, the public, as well as those people whose livelihoods depend on film, will lose out.
"So we applaud the decision and look forward to working with the ISPs and the Government to keep the pressure up on the pirates and help safeguard the future of the industry."
Christine Payne, chairwoman of the Creative Coalition Campaign, a partnership between trade unions representing workers in the creative industries and organisations in the music, film, TV, publishing and sports sectors, said: "Thousands of businesses and millions of workers now know that the law of the land applies to the internet.
"Online copyright theft deprives businesses of up to 20% of their revenues every year. Finally, this little known law will help us to protect our property."
Richard Mollet, chief executive officer of The Publishers Association, said: "This is a great result and will benefit the whole of the creative sector.
"Online infringement has been allowed to run unchecked for far too long, damaging jobs and growth.
"It is satisfying to see that the Copyright Act gives the creative sector the ability to fight back."
Mr Justice Arnold said in his written judgment that the case was about the legal remedies that can be obtained to combat online copyright infringement.
The studios sought an injunction against BT under the CDPA which in essence was "intended to block or at least impede access by BT's subscribers" to Newzbin2.
He said: "The studios have made it clear that this is a test case: if they are successful in obtaining an order against BT, then they intend to seek similar orders against all the other significant ISPs in the UK."
Operators of the Newzbin2 website were unknown, but the operation appeared to have moved offshore and was "thus effectively beyond the reach of this court".
The judge said the website provided the means for "continued large-scale infringement of the studios' copyrights".
It was contended by the studios that, in those circumstances, the only way in which they can obtain "effective relief to prevent, or at least reduce the scale of, these infringements" was by means of an order against BT "and thereafter the other ISPs".
The problem of online copyright infringement "is by now a very well-known one", said the judge.
The studios relied on two recent studies of the scale of the problem relating to the film and television industries.
One study by Ipsos MediaCat in April 2010, analysing the scale of film and television piracy in the UK in 2009, estimated the overall loss from film piracy at £477 million and the overall loss from television piracy at £58 million.
A March 2010 study by Tera Consultants concluded that in 2008 the audio and audiovisual industries in the UK lost almost 670 million euros in revenues to physical and digital piracy, with the larger proportion of that lost revenue attributable to digital piracy.
The application by the studios "represents an attempt by copyright owners indirectly to enforce their rights in circumstances where direct enforcement has been tried and failed", said the judge.
He said it should be emphasised that BT "does not provide any services to the operators of the Newzbin2 website "and in particular it does not 'host' the website".
BT contended that the court had no jurisdiction to make the order sought by the studios, but the judge announced today that he had concluded that it does.
He said he did not "anticipate a flood of such applications"
The judge ruled that the order sought by the studios was a "proportionate" one and "the cost of implementation to BT would be modest and proportionate".
Mike O'Connor, chief executive of Consumer Focus, said: "Website blocking only treats the symptoms, not the cause of why consumers infringe copyright.
"Blocking access to Newzbin2 is shortsighted and will not reduce demand for Hollywood movies. Consumers will seek out other sources and the only long term solution is more and better legal alternatives."
PA
