He will replace Martin Bean, who is returning to his native Australia at the end of this year to become vice-chancellor of RMIT University in Melbourne.
Since graduating from the University of Cambridge, Mr Horrocks has spent his entire career to date at the BBC, editing programmes such as Panorama and Newsnight before becoming head of TV news and then, in 2009, director of the World Service.
He will be the second non-academic to run the OU, following Mr Bean, a former general manager at Microsoft.
Mr Horrocks said it was a “profound honour” to join the OU “at such an interesting time for the sector”.
“I have seen first-hand the transformative power of learning around the world, especially when coupled with technology,” he said.
“The Open University has been making a life-changing difference to hundreds of thousands of people by providing them, through distance learning, with an education that may otherwise have been unattainable.”
Richard Gillingwater, the OU’s pro-chancellor designate and the chairman of the selection panel, said Mr Horrocks had been “the stand-out candidate in a very strong field”.
“Like the higher education sector, the BBC has had to adapt to new ways of working and funding over recent years, so Peter brings with him not only a wealth of relevant experience, but the drive, vision and intellect to lead the OU into the future,” Mr Gillingwater said.
With Mr Horrocks not due to take up his new post until May 2015, the role of acting vice-chancellor will be taken in the interim by Tim Blackman, currently the pro vice-chancellor for research, scholarship and quality.