The University of Houston professor describes her field as “the study of courage, shame, vulnerability and empathy” and has written a string of best-selling motivational books.
Speaking at an online event discussing social media and its potential as a force for good, Harry said he and Meghan are big fans of Brown's work.
The event was hosted by the Queen's Commonwealth Trust, of which the duke and duchess are president and vice-president respectively.
Among the guests was Hunter Johnson, founder of The Man Cave – an Australian organisation working to encourage healthy masculinity in men and boys.
While speaking with Harry and Meghan, Johnson quoted one of Brown's philosophies, saying: “Vulnerability brings connection and connection is why we are here. It brings meaning and it brings purpose to our lives.”
He also referred to Tristan Hunter, co-founder of the Centre for Humane Technology, which works to promote the positive evolution of social media, rather than platforms that “hijack” users' attention.
Hunter coined the phrases “human downgrading” and “system of harms” to describe the methods social media relies on, including addiction, distraction, isolation, polarisation and fake news.
As Johnson spoke, Harry smiled and turned to look at Meghan, before saying: “I love the fact you're quoting Brené Brown and also quoting Tristan Harris because they are two people we absolutely adore as well, and we know.”
The duchess laughed, adding: “We love them!”
Harry continued: “Five years ago, six years ago, talking about your mental health was a sign of weakness. Just as much as vulnerability was a form of weakness.
”If we're all able to show our vulnerability that doesn't mean you are weak, if anything I believe that shows mostly your strength.
“If you are so in-touch with your emotions that you know where you are on each day, well that's a superpower.”
Meghan was already known to be an admirer of Brown’s, having included an article titled Speak Your Truth. Follow Your Wild Heart, in her guest-edited issue of British Vogue.
The comments follow a recent article written by Harry in which he called for social media companies to reform how they work with advertisers, explaining that many platforms are stoking a “crisis of hate”.
Writing in the American business publication Fast Company, Harry said: “The digital landscape is unwell and companies like yours have the chance to reconsider your role in funding and supporting online platforms that have contributed to, stoked, and created the conditions for a crisis of hate, a crisis of health, and a crisis of truth.”
The 35-year-old also questioned how social media platforms use data, writing: “Every time you click they learn more about you. Our information, private data, and unknown habits are traded on for advertising space and dollars.
“The price we’re all paying is much higher than it appears. Whereas normally we’re the consumer buying a product, in this ever-changing digital world, we are the product.”
Harry and Meghan also recently backed a campaign calling for businesses to pause advertising on Facebook due to the platform’s failure to combat online hate speech.
The Stop Hate for Profit campaign asked companies to boycott Facebook throughout July as a show of “solidarity with our most deeply held American values of freedom, equality and justice”.