
Davie will take charge of an annual budget of more than £200m and will oversee BBC Radios 1, 2, 3, 4, 5 Live and digital radio stations 1Xtra, 6 Music, BBC 7, 5 Live Sports Extra and the Asian Network.
He will also be responsible for the three BBC orchestras in England, the BBC Proms, Classical Music and Performance Television and Radio Resources, as well as Radio Drama, Television Music Entertainment and all audio across the BBC.
Prior to joining the BBC in 2005, Davie was vice-president of marketing and franchise at PepsiCo Europe. He replaced Andy Duncan, who moved from the BBC to Channel 4 to become chief executive.
Abramsky will leave at the end of September, when she will take up the chair of the Heritage Lottery Fund.
Davie said: 'As a passionate advocate of radio, I am excited by the challenge of continuing to deliver not only distinctive BBC services, but also to support the growth of the medium as a whole across traditional and digital platforms.'