Abramsky has run the corporation's national radio stations since 1999, before which she was head of the BBC's continuous news department.
She was responsible for setting up Radio 5 Live, News 24 and News Online. She has also been editor of Radio 4's 'Today', 'PM' and the 'World at One'.
Abramsky joined the BBC in 1969 as a programmes operations assistant and in 1986 took over the station's flagship morning news programme 'Today'.
The following year, Abramsky took control of news across all BBC radio networks. In 1991, she set up a rolling news service during the first Gulf War, which became a precursor to Radio 5 Live, which was established three years later.
In recent years, Abramsky launched the Electric Proms live music event and in 2001, she was appointed a CBE for services to radio.
In an email sent to BBC staff yesterday Mark Thompson, BBC Director-General, said: "Her contribution to the BBC has been immense and she will leave a precious and lasting legacy.
"She leaves BBC Radio in remarkable health with record audience figures and an exciting digital future already in place."
In her own email to staff at the BBC, Abramsky said: "While this is a wonderful opportunity, it will be a great wrench for me to leave the BBC. I have spent my working life here, the vast majority of it in radio, and I am as passionate about it now as when I joined as a programme operations Assistant 39 years ago.
"I have always believed that the BBC is the most important cultural institution in the UK. Its willingness to take risks, its ambition that permeates through its programmes and schedules, and the unsurpassed quality of its news output demonstrates every day that it can and does make a difference."
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