She will start in May, succeeding Sir Tom Shebbeare who left the youth charity in Autumn 2003 after 16 years to become Prince Charles' director of charities.
Milburn, 46, has a reputation for transforming the organisations she leads. Since she joined Children in Need in July 2000, the charity has raised more than £100m for disadvantaged children, increasing its annual income from £16m to £30m.
At spinal injuries charity Aspire, where she spent seven years as chief executive, Milburn increased staff levels from five to 100 and was in charge of developing the first training centre for able-bodied and disabled people in Europe.
Yet when she applied for the top job there, she had little experience as a charity executive and the charity's chairman, Peter Stanford, recalled that he had to convince the board of trustees that she was the best candidate.
"She makes people want to do things for her, and that is what is most important if you want to be a leader," he said.
Milburn began her career at the Press Association in 1976 and was the first woman to be offered journalism training by the organisation. Her first voluntary sector role was setting up Cafod's press office in the mid-1980s. Clare Dixon, head of programmes in Latin America and Caribbean countries at Cafod, remains a close friend.
"She is a larger-than-life person, a really effervescent character," Dixon said. "She relates to people very well and is a great motivator.
I think she will be a breath of fresh air for the Prince's Trust."
Sir Robert Smith, BBC governor and chairman of the BBC Children in Need Appeal, said: "Everyone associated with the appeal, both inside and outside the BBC, values Martina's warmth, determination and creativity.
"She leaves the appeal significantly stronger and we are therefore confident that the post will attract high-quality candidates."