The annual event, which took place in Glasgow in 2009, 2011 and 2013, had been screened by BBC3 in recent years but the corporation's commitment will in future be limited to radio.
Kanye West, Jay-Z and Emile Sande are among the high-profile artists who have appeared at the awards since their launch in 1996.
The BBC is holding its own major music awards event in December. This year's Mobo ceremony is to take place on October 22. It will now be shown on digital channel ITV2, with a highlights show to be screened on the main ITV channel.
Founder of the awards Kanya King said of the new three-year deal: "We are very excited that, with our new broadcaster, the awards show will be receiving more support and attention than ever before."