Baroness Patricia Scotland, the first woman to be appointed Commonwealth secretary-general, says she will "put the women's agenda very strongly on the table".
Commonwealth leaders meeting in Malta chose Scotland on Friday after a fraught and extended meeting to choose between three candidates.
She is to take over from Kamalesh Sharma, who has served in the role for eight years.
Scotland, a lawyer who has dual British and Dominican citizenship, served as minister of state, deputy home secretary and attorney-general under the previous Labour government in the UK.
She was the first black woman to be appointed as a Queen's Counsel in the UK and at the age of 35, was also the youngest woman.
After Malta's Prime Minister Joseph Muscat announced her appointment to reporters, she said she was "incredibly proud" to be the first woman to hold the post.
"I do wish to put the women's agenda very strongly on the table," she said.
"Domestic violence affects one in three women globally, it is the greatest cause of morbidity in women and girls and it is a disgrace that that is so."
Scotland said that in the UK a partnership effort by central government, local authorities, business, charities and civil society managed to reduce domestic violence by 64 per cent and the economic cost of it by more than STG7 billion.
"That's an aspiration I want for every single country in the Commonwealth".
The secretary-general designate said that as a "true daughter of the Commonwealth" through her Caribbean and African ancestry she was determined to work respectfully with the 53 nations of the global grouping to tackle a raft of issues.
She said the threat of climate change was real, particularly for island nations in the Caribbean and the Pacific, and next week's climate talks in Paris were an opportunity to "put the world on a different path".
When asked what she felt about whether the next head of the Commonwealth should be Prince Charles or someone elected, Scotland said that was a decision for the 53 members of the Commonwealth, not her.
The two candidates who missed out on the job were Sir Ronald Sanders, Antigua's ambassador to Washington, and a second female candidate, Botswana's Mmasekgoa Masire-Mwamba, who has been deputy secretary-general of the Commonwealth.
When a straw poll failed to deliver a clear winner, the chair of the meeting, Dr Muscat, cleared officials from the room and extended the meeting among leaders only until a consensus on the new appointment was reached.
Before Friday's vote there had been speculation that former Coalition foreign minister Alexander Downer could be given the post as a "compromise candidate" to avoid divisions over the other candidates.
Mr Downer, who is Australia's high commissioner in London, has been in Malta over the past few days standing in for Julie Bishop at a meeting of Commonwealth foreign ministers.
