Cressida Dick is to become the first ­female head of the Metropolitan police, completing a remarkable career comeback by vowing to reform Britain’s largest police force.

The former senior Scotland Yard officer – who had quit policing to take up a job in the Foreign Office – won the support of the home secretary, Amber Rudd, and the London mayor, Sadiq Khan, to take on the running of a police force that dates back to 1829.

Flanked by the Conservative and Labour politicians, Dick, 56, stood outside New Scotland Yard to say it was “an extraordinary privilege” and that she was “very humbled” to be chosen for the post, which pays £270,000 a year.

Sources close to Khan said that of the four candidates for the job, it was Dick who outlined the best vision for reforming the Met while keeping the capital safe, during two rounds of interviews. The source added Dick “accepts that there needs to be changes”.

Her ascent to the top job is all the more remarkable because her career in policing had seemed over. She will replace Sir Bernard Hogan-Howe, with whom there had been tensions which led to her moving from the role she loved as the Met’s head of counter-terrorism and departing from the force.

Dick also becomes first commissioner of the Met in the modern era to get the job despite never having led a police force previously. She had applied and failed to get the top job with the Police Service of Northern Ireland, eventually landing a role as a director general in the Foreign Office.

The incoming commissioner faces a budget crisis, with the Met having to save hundreds of millions of pounds whilst contending with political and public pressure to maintain officer numbers on the streets and amid findings from the official police inspectorate that it is struggling to deal with regular crimes.

Dick is regarded within policing as being one of the best of her generation, operationally, with a strong sense of ethics. Dick will have to be resworn in as a police officer, a legal requirement of being commissioner. Hogan-Howe formally steps down next week after five-and-a half years in charge, and his deputy Craig Mackey may fill the vacancy until Dick can start work.

But Dick has also been associated with one of the biggest disasters in policing, when in 2005 she commanded an operation that saw an innocent man, Jean Charles de Menezes, mistaken by officers for a wanted terrorist and shot to death.

His family immediately criticised the appointment. Patricia Armani, de Menezes’ cousin, said they doubted Dick could command public confidence: “We have serious concerns about the appointment … At the helm of the police on that fateful day when Jean was killed was Cressida Dick. The message of today’s appointment is that police officers can act with impunity”.

A jury at a criminal trial in 2007 had exonerated her of any personal blame but some thought her role in the incident could block her becoming leader of the Met.

Rudd hailed Dick’s appointment and set out some of the challenges faced: “She now takes on one of the most demanding, high-profile and important jobs in UK policing, against the backdrop of a heightened terror alert and evolving threats from fraud and cybercrime. The challenges ahead include protecting the most vulnerable, including victims of sexual abuse and domestic violence.

“Cressida’s skills and insight will ensure the Metropolitan police adapt to the changing patterns of crime in the 21st century and continue to keep communities safe across London and the UK.”

Theresa May said Dick had “an outstanding record of public service” and “the exceptional qualities needed to meet the challenge of leading the Met”. The prime minister added that her skills and insight “will be crucial in shaping the Met as the job of police reform continues, coordinating the national response to the ongoing threat of terrorism and serious criminality as well as keeping Londoners safe. In addition, she will be a champion of the most vulnerable who the police are there to protect”.

Khan had early on identified Dick as his chosen candidate to be Met commissioner. He said: “She has already had a long and distinguished career, and her experience and ability has shone throughout this process.

“This is a historic day for London and a proud day for me as mayor … it was absolutely essential that we found the best possible person to take the Met forward over the coming years and I am confident that we have succeeded.”

The selection process saw the four final candidates subjected to long psychometric tests and two gruelling interviews. Dick faced competition from the current Met head of counter-terrorism, assistant commissioner Mark Rowley, who had replaced Dick in that role and who was seen as the preferred candidate of Hogan-Howe.

Met veteran Stephen Kavanagh, currently chief constable of Essex, is seen as having boosted his reputation during the selection process and will be a strong contender next time. Sara Thornton, the current chair of the National Police Chiefs’ Council also made the final four.

Dick was a protege of the former Met commissioner Lord Blair, and is the child of Oxford University academics. Like every police chief before her, she began as a beat officer in 1983, rising through the ranks to become assistant commissioner in 2009.

She was head of counter-terrorism for the London 2012 Olympic Games but before that she oversaw the launch of the Met’s inquiries into phone hacking and bribing of officials, which led to a string of prosecutions.

Dick’s appointment means five of the top posts in the criminal justice system in England and Wales are now held by women. Lynne Owens is director general of the National Crime Agency, seen as a rival to the Met for prestige. The other women leading the justice system include Alison Saunders at the Crown Prosecution Service, Rudd and Thornton.

In all, six candidates applied to be commissioner. It was the first time foreign police chiefs would be considered but none applied despite the government changing the law. The Guardian understands that one US police chief was sounded out but declined to apply.