The movement is closely associated with the Twitter campaign #MeToo that began after actress-activist Alyssa Milano tweeted: "If you've been sexually harassed or assaulted write 'me too' as a reply to this tweet."
It was tweeted nearly a million times in 48 hours by people sharing their stories and denouncing sexual harassment.
But Time says the hashtag is "part of the picture, but not all of it".
"This is the fastest moving social change we've seen in decades," editor-in-chief Edward Felsenthal said.
He told NBC's Today programme: "It began with individual acts of courage by hundreds of women - and some men, too - who came forward to tell their own stories."
More than 50 women have publicly accused film producer Weinstein of sexual harassment, assault, rape, and inappropriate behaviour in incidents spanning four decades.
Time magazine's tradition began in 1927 as 'Man of the Year' but changed to Person of the Year in 1999.
The award, decided by Time’s editors, is given to the person who "for better or for worse has done the most to influence the events of the year."
The majority of winners have been individuals but in 2014 "Ebola fighters" were recognised and in 2011 "The Protestor" acknowledged the Arab Spring.