“I recognize the absurdity of so much wealth being concentrated in the hands of one person, and I believe the only responsible thing to do with a fortune this size is give it away—as thoughtfully and impactfully as possible,” Ms. French Gates wrote in her new letter.

The Gates Foundation is one of the world’s largest philanthropies with an endowment topping $50 billion. In July, Mr. Gates and Ms. French Gates said they would commit a further $15 billion to the endowment. It is possible that Ms. French Gates makes additional donations to the foundation even as she gives to other charities, one of the people familiar with the matter said.

A foundation spokeswoman declined to comment beyond prior foundation news releases and the Giving Pledge letters. She said foundation chief executive

Mark Suzman

had no comment.

The foundation recently added four members to its board of trustees in an effort to boost governance following its co-founders’ divorce. Ms. French Gates and Mr. Gates are the foundation’s co-chairs, though she has agreed to resign in 2023 if either of them decides they can no longer work together. Billionaire

Warren Buffett,

another major donor, was a trustee until he resigned in June 2021.

In a Gates Foundation video call on Wednesday, Mr. Suzman said Ms. French Gates and Mr. Gates are fully committed to being the long-term co-chairs of the foundation. He said the co-founders regularly lead the foundation’s Covid-19 response meetings and jointly approved recent expanded investments in areas like gender equality and climate adaptation.

Ms. French Gates, Mr. Gates and Mr. Buffett started the Giving Pledge in 2010 to try to kick-start a new era of philanthropy. The campaign encourages the world’s richest individuals and couples to give more than half of their wealth to philanthropy or charitable causes, either during their lifetime or in their wills. Participants typically share their philanthropic intentions in a letter published online.

In late November, Mr. Gates and Ms. French Gates posted new, individual Giving Pledge letters.

In her letter, Ms. French Gates recommitted to giving away the majority of her wealth but didn’t specify that it would go to the Gates Foundation. “I think philanthropy is most effective when it prioritizes flexibility over ideology—and why in my work at the foundation and Pivotal Ventures I’ll continue to seek out new partners, ideas, and perspectives,” she wrote.

Ms. French Gates launched Pivotal Ventures in 2015 to focus on issues affecting women and families in the U.S., including paid-leave policies, and getting more women in technology and to run for public office. Ms. French Gates said in 2019 she would commit $1 billion over a 10-year period through Pivotal to promote gender equality.

Mr. Gates, in his most recent letter, reiterated that most of his wealth will go toward philanthropy, specifying that it will be through the Gates Foundation. “The foundation is my top philanthropic priority, even as my giving in other areas has grown over the years—primarily in mitigation of climate change and tackling Alzheimer’s disease,” he wrote.

Mr. Gates has championed eradication of polio and malaria at the Gates Foundation. He has also invested in clean energy and other technologies to address climate change, as well as Alzheimer’s research through his company Gates Ventures and other investment vehicles.

On Wednesday, Mr. Suzman said that the foundation’s new board will have its first meeting next week. The new members are: Mr. Suzman; businessman and philanthropist Strive Masiyiwa; economist Baroness Nemat “Minouche” Shafik; and philanthropic consultant Thomas J. Tierney.

In response to a question about whether board members will challenge the way the foundation works, Mr. Suzman said it remains a family foundation. “We’ve been clear and they’ve been clear with the incoming board members that we are not looking to change our mission or change our priorities,” he said.

Mr. Suzman said, however, that given the resources the foundation has it can be difficult to get honest feedback so that will be a key role for board members. “Many of our partners are not really incentivized to give us hard feedback or honest dialogue because they’re often looking for partnership or resources,” he said.

Mr. Suzman also said the foundation purposefully selected board members that had worked with Mr. Gates and Ms. French Gates, as well as with the foundation, so trustees were familiar with how the foundation operates.

Write to Emily Glazer at emily.glazer@wsj.com