London Mayor Sadiq Khan, who describes himself as a "proud feminist," said he hoped that the statue would be an inspiration to those fighting for gender equality.
He said it was an opportunity to celebrate but also to "take stock and to acknowledge that the original goal of gender equality hasn't been reached."
Khan added: "It's simply not right that this historic square has been a male-only zone for statues, because statues matter. They are a symbol of our values, the demonstration of the importance we place on hard battles won, both in peace and war, and an expression of who and what we chose to celebrate."
Britain is marking the centennial of (some) women getting the right to vote - in 1918, women older than 30 who owned property in Britain achieved the right to vote. It was also the year that women were allowed to stand for election as a member of Parliament for the first time. (The first woman to take her seat in Parliament was Nancy Astor, an American who moved to the UK when she was 26.)
Fawcett was a leading figure in the campaign in the long fight for women's right to vote. Born in 1847 in coastal town of Aldeburgh, Fawcett was interested in women's suffrage, even as a teenager.
When she was 19, she organised signatures for a petition calling for votes for women (she was too young to sign it herself). She became well-known as an advocate for peaceful protests and in 1897 became president of the National Union of Women's Suffrage Societies. She also campaigned for equal access for higher education.
She died in 1929, a year after voting rights were extended to all women older than 21.
The new 2.5m statue by Gillian Wearing is the first statue in the square to be designed by a woman.
The statue is holding a placard that reads "courage calls to courage everywhere" - a quote taken from a speech Fawcett gave following the death of suffragette Emily Wilding Davison who was fatally injured at the Epsom Derby horse race in 1913.
The unveiling follows an online petition started by the writer and activist Caroline Criado Perez, whose previous campaigning work led to Jane Austen appearing on Britain's 10-pound bank note.
Criado Perez said she began the campaign for a woman statue after she went jogging through the square on International Women's Day in 2016 and noticed that all of the monuments were men.
At the unveiling today, she said: "Women are still woefully underrepresented, but we are making one hell of a start in changing that."
