The agreement brings to a close negotiations which began as early as June last year, and which saw a preliminary memorandum of understanding signed between the two companies in March.
The new station will be run by the Arabian Radio Network, a subsidiary of the government owned AMG, and will broadcast from the network's offices in Dubai.
Sir Richard Branson's Virgin Group will not be involved in the day-to-day running of the station, but will oversee programming, marketing and promotions.
Branson, who is chairman of the Virgin Group, said: "Virgin Radio is experiencing phenomenal growth at the moment, having announced launches in Italy, France and now Dubai in the last two months alone.
"We are already exploring opportunities to establish Virgin Radio in other parts of the Middle East and I have no doubt that we'll be launching many more stations over the coming years."
Abdul Latif Al Sayegh, chief executive of Arab Media Group, said: "We have a vision of filling the many niches that have been left unaddressed in popular media up to this point, and through better understanding and knowledge of our audience we will keep delivering. Virgin Radio is a major step towards achieving this vision."
The news that Virgin Radio planned to launch in the Middle East market was first announced in ±±¾©Èü³µpk10 Middle East magazine last year, with Mark Fisher, CEO of Virgin Radio International, revealing that the conditions were then right for a Virgin Radio station.
A number of broadcasters were understood to have been in the running for the deal, including the fledgling Fujairah Media and Dubai-based Radio 1 and 2.
AMG is also set to launch MTV Arabiya later this year.