The deal means that Zuckerberg will avoid having to testify in a court in Delaware, where he had been scheduled to appear on Monday to explain to a judge precisely why Facebook changed its mind on the share reclassification.
"Following extensive, arms-length negotiations, the company has agreed, in the exercise of business judgement, to resolve the fees and expenses motion," judge J Travis Laster wrote.
"Defendants continue to deny any and all allegations that they engaged in wrongdoing in any way, and the company has agreed to resolve the motion due to the costs of defence of that application and litigation risk."
Facebook declined to comment on the outcome of the case.
In 2015, Zuckerberg pledged to sell or give away 99pc of his Facebook stock during his lifetime in order to found the Chan Zuckerberg Initiative, a charitable foundation he created with his wife Priscilla Chan.
Zuckerberg already controlled a majority of Facebook's voting rights through its special class B shares, but proposed to further dilute the company's voting stock so that he could sell off his stake while retaining control.
Investors objected, and Zuckerberg abandoned the plan just four days before he was due to testify in that lawsuit, claiming that it was no longer necessary because Facebook's stock had grown so valuable that he could sell enough to "fully fund" his philanthropy without losing control.
The investors argued that they should get the credit for this outcome, achieved through "hard-fought litigation", and demanded that Facebook pay their lawyers a percentage of the value they said they had created for its shareholders.
But Facebook contended that because Mr Zuckerberg had never set out an exact timescale for giving up control, the investors could not demonstrate that they had created any value and therefore deserved much less.
The 34-year-old's control of Facebook came under renewed attack last week after revelations that it had used "dark arts" PR firm with its own "in-house fake news shop" to spread negative information about its critics.
On Friday investors called for Zuckerberg to step down as chairman of Facebook's board, warning that his dual role had created a "concentration of power" that led it to hide from its problems.
Facebook said that it had never asked the PR firm in question, Definers, to publish any "misinformation", and Mr Zuckerberg said he had terminated Facebook's relationship with the firm as soon as he found out about it.
- Telegraph