Qatar-based beIN, which had been the motor sports' exclusive broadcaster in the region since 2014, paid an estimated US$30-40 million a year during the five year deal.
The sport, owned since 2017 by US-based Liberty Media, in June past year said that it was investigating alleged illegal broadcasts of its content in the Middle East and North Africa.
The decision is a outcome of the drawn-out battle between BeIN and pirate broadcaster BeoutQ, which has been stealing BeIN's content for more than a year and is now the subject of a US$1 billion worldwide investment arbitration brought against Saudi Arabia last October.
BeIN has repeatedly complained about this, pointing out beoutQ's ties to the Saudi regime, with whom Qatar is locked in a bitter diplomatic dispute.
BeoutQ is widely available in Saudi Arabia but Riyadh says it is not based there and that the authorities are committed to fighting piracy.
Tom Keaveny, BeIN's managing director in the region, said that the company will "pay less" for broadcast rights in the future in an effort to combat "industrial-scale theft" carried out by the Saudi group.
Tom Keaveny, beIN Media Group's managing director, said the broadcaster had, for almost two years, warned of the commercial impact of piracy after paying huge sums for media rights.
BeIN has walked away from F1 over a lack of action taken over piracy in the region, particularly by the Saudi-based beoutQ.
Shortly after last summer's World Cup, three leading technology companies issued reports saying beoutQ is being broadcast on Saudi-controlled Arabsat satellites and, in October, the Qatari government launched a case against its neighbour at the World Trade Organisation, claiming more than one billion U.S. dollars (£775million) in compensation.
A Formula One insider said that the beIN contract was originally a sublicense agreement with MP & Silva, a sports marketing and media rights company that went into administration late past year.
Richard Broughton from Ampere Analysis told Bloomberg: "Gulf operators are under intense pressure at the moment from piracy and poor consumer receptiveness to paying high monthly fees for content".
Formula One (F1), which was bought by Liberty Media in 2017, confirmed tocnews agency Bloomberg it was finalising arrangements with a new licensee for MENA. A new grand prix will be held in Hanoi, Vietnam from 2020, adding to F1's existing Asian races in Singapore, China and Japan.
Formula One launched its own over-the-top (OTT) streaming service last season and aims to grow the platform to around two million subscribers by 2027.