The Premier League announced the agreement with the international media agency on Thursday, the latest in a series of rights deals expected to bring the League a total windfall of more than 5 billion pounds ($7.9 billion) in 2013 though 2016.
ADM previously held the rights and had been expected to fight hard to retain them, since Premier League Champions Manchester City are owned by Sheikh Mansour Bin Zayed Al Nahyan, a member of Abu Dhabi's ruling family.
Qatar-based Al Jazeera has also been building up its sports broadcasting business, launching channels in France and the United States, and had been expecting to bid strongly for the Premier League rights in its home region.
MP & Silva CEO Andrea Radrizzani said the big two broadcasters did not bid as aggressively as he had feared.
"Our price was quite near what ADM paid in the past," Radrizzani told Reuters. "Even though the price was quite high, we thought it was killer content for the region."
The rights cover all 380 Premier League matches per season and extend across 23 countries from Iran to Morocco, taking in the United Arab Emirates and Egypt.
Having bought the rights, MP & Silva will seek to do its own deals with broadcasters in the region to show live action.
Viewers in some countries may not need to adjust their television sets to receive new channels because MP & Silva plans to negotiate with ADM and Al Jazeera.
The Premier League is the richest in the world in terms of TV revenue and outperforms Spanish and German rivals when it comes to selling overseas.
"There is a lot of appetite for football and the Premier League is the best league in the world," said Radrizzani.
"The format is very good for the region in terms of time slots at the weekend," he added. ($1 = 0.6350 British pounds)