Three government departments settled the claim, brought by Ella Adoo-Kissi-Debrah's estate, for "an undisclosed sum" ahead of a High Court trial, the law firm representing the family revealed.
The legal action argued the young girl's right to life under the Human Rights Act had been breached.
"Ella's suffering and death were a tragedy," ministers from the departments wrote in a letter to her mother Rosamund Adoo-Kissi-Debrah.
"We again take this opportunity to say we are truly sorry for your loss," they added. "To lose a loved one at such a young age is an immeasurable loss."
The ministers said in the letter that Britain's new Labour government, elected in July, was committed to tackling air pollution with "a comprehensive and ambitious" strategy.
"We are also conducting a comprehensive review of how we communicate air quality information to ensure members of the public and vulnerable people have the information they need to protect themselves," it added.
Ella Adoo-Kissi-Debrah, from southeast London, died of acute respiratory failure in February 2013 following a serious asthma attack, after being exposed to poor air quality for much of her life.
She lived in southeast London just 30 metres (33 yards) from a major ring road in the British capital which is often clogged with heavy traffic.
She had been taken to hospital nearly 30 times with breathing difficulties in the years prior.
In a legal first, coroner Philip Barlow ruled in December 2020 that pollution from vehicle emissions made a "material contribution" to her death.
His report urged the UK to introduce legally-binding air pollution targets based on World Health Organization guidelines, which has now happened.
Rosamund Adoo-Kissi-Debrah and Ella's siblings met Thursday with a junior environment minister, Emma Hardy, as part of the settlement.
"I have told Ms Hardy today that so much more needs to be urgently done to improve our air quality," Rosamund said in a statement.
She added that she was "ready to assist" with "what has become a public health crisis".
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