Carrie Gracie quit her role as China editor in January in protest at pay inequality with male colleagues.
The broadcaster says it apologises for underpaying the journalist and has now “put this right”.
Gracie will give the full amount of back pay she has received to a charity to set up a fund for women needing legal advice on equal pay claims.
In a statement, the corporation said: “The BBC acknowledges that Carrie was told she would be paid in line with the North American editor when she took the role of China editor, and she accepted the role on that understanding.
“The BBC acknowledges the specific circumstances relating to Carrie’s appointment, apologises for underpaying Carrie, and has now put this right. Carrie is donating the full amount received to a charity of her choice.”
Gracie said: “I am glad to have been able to resolve this with the director general, it shows that we can make progress.
“For me, this was always about the principle, rather than the money. I’m delighted to donate all the backdated pay from the BBC to help women striving for equality at work.”
Following her resignation as China editor, Ms Gracie – who has been at the BBC for more than 30 years – accused the corporation of having a “secretive and illegal pay culture” in an open letter.
She said the BBC was facing a “crisis of trust”, after it was revealed two-thirds of its stars earning more than £150,000 were male.
Speaking to the Commons culture committee in January, Ms Gracie described how – after she submitted a grievance over her pay last year – the BBC told her she had been “inadvertently underpaid” since 2014.
That was the same year Jon Sopel was appointed the BBC’s North America editor. He earns between £200,000 and £249,000, compared to Gracie’s salary of less than £150,000.
Gracie revealed she believed she had “won a commitment to pay parity” when accepting the China role in December 2013.
She explained this was why she got “such a shock” when the BBC was forced to reveal Mr Sopel’s pay and the salaries of other top-earning stars last year.
Gracie will now take up to six months of unpaid leave at her own request, using the time to write and speak on both China and gender equality.