The 14-year-old Stranger Things actress joins Prince Harry, Meghan Markle and rapper Cardi B on the 2018 list.
She is the youngest person to be included in Time's top 100, which is published every year.
Brown rose to fame with her role as the character Eleven in the hugely popular science fiction TV show. She starred in the first series when she was 12.
Other famous figures who made the Time magazine list include singers Rihanna, Kesha and Shawn Mendes as well as US President Donald Trump and North Korean leader Kim Jong-un.
Tennis player Roger Federer, actress Nicole Kidman and Scottish Tory leader Ruth Davidson also feature among the 100 along with Mayor of London Sadiq Khan.
Writing an appreciation of Brown for Time magazine, US actor Aaron Paul called her an "extraordinary" actress.
"She may have been 12 in years, but her spirit and mind were timeless," he said, speaking of first meeting the teenager in New York.
"A wise woman was speaking from her cherubic face.
"It was like speaking to a future mentor with a perspective and groundedness that I could only have dreamed of at that age. Or at any age, if I'm being honest."
Mr Paul added: "Maybe that's why she's such an extraordinary actor.
"She somehow understands the human experience as if she has lived it for a thousand years. I'm proud to know her. To call her a friend. To call her my adopted daughter."
Brown, whose parents are British, has 2.2 million followers on Twitter and 16 million on Instagram.
In July last year she used her large social media reach to launch an anti-bullying campaign.
She tweeted encouraging messages to fans who had shared their stories of bullying.
After Time announced the list, Brown's fans praised her inclusion on social media.
For a girl of her age to "have so much maturity" is "pretty incredible", one person said on Twitter.
Weekly news magazine Time is read by millions of people around the globe.
It is perhaps best known for its prestigious "Time Person of the Year" award which first began in 1927 as "Man of the Year".
Past recipients have included Queen Elizabeth II and Mark Zuckerberg as well as, controversially, Adolf Hitler in 1938.
Prince Harry and Meghan Markle both made 2018's Time 100 list -- Photo: EPA |
In his tribute to Prince Harry for this year's Time 100 list, singer Elton John said it has been a "joy" to see Harry "grow to inherit his mother's warmth, sense of humour and courage to stand up and champion the causes he truly believes in".
"Prince Harry has that rare ability to walk into a room full of strangers and make everyone feel comfortable and at ease," the performer added.
Who else made the 2018 Time magazine list?
Among those featured are:
A group of Florida students who have been campaigning for gun control following the Parkland school shooting
Hugh Jackman, actor
Greta Gerwig, actress and director
Guillermo del Toro, director
Justin Trudeau, Canadian prime minister
Robert Mueller, US special counsel
Xi Jinping, president of China
Leo Varadkar, Irish Taoiseach (prime minister)
Emmerson Mnangagwa, president of Zimbabwe
Shinzo Abe, prime minister of Japan
Emmanuel Macron, president of France
Jennifer Lopez, musician and actress
Christopher Wylie, Cambridge Analytica whistleblower
Virgil Abloh, fashion designer
Oprah Winfrey, TV presenter
Jeff Bezos, founder and CEO of Amazon
Elon Musk, entrepreneur
Sonia Friedman, West End and Broadway theatre producer
Source: BBC