Ms McCormack, who was in her late 60s and lived in Derry, formerly directed the Northern Ireland section of the trade union UNISON, as first female regional secretary.
During her lifetime, she achieved many firsts for women - she was the first female full-time official of the National Union of Public Employees and served as the first female President of the Irish Congress of Trade Unions.
The Belfast native also played a pivotal role in the behind-the-scenes discussions which led to the signing of the Good Friday Agreement.
Mrs Clinton said she was deeply saddened to hear of the death of Mrs McCormack, whom she said "promoted peace and reconciliation in her beloved Northern Ireland and around the world".
"Until her final days, she never stopped promoting peace, human rights and equality. She travelled the world encouraging young women to be agents of change in their communities and countries.
"I recently visited Northern Ireland and saw the legacy of her work," said the US representative.
"There is more we must do to build lasting peace and prosperity in communities, but we have come so far in part because of her insistence on a seat at the table for women and others who have been marginalised."
Mrs Clinton said her friend met the "tremendous" challenge of mending communities with joy.
She challenged women and men to find a way to put aside their differences, move past hurt and anger, and work together to end violence and build a fair and lasting peace.
Patricia McKeown, Regional Secretary UNISON, described her passing as "the sad day thousands of workers and trade union members have been dreading".
"She has touched the lives of thousands of ordinary women and men and she has succeeded in what she set out to do. She has made a difference.
"Much has been said and written about Inez over the years. She is held in the highest regard across the International Trade Union movement."
Ms McKeown added: "In the union we have always known her true worth. It lies not solely in her remarkable journey, engaging with power systems dominated by disrespect for women in general and the working class in particular.
"It lies especially in her unselfish and unshakable belief that ordinary people, given a chance, can change the world."
Ms McKeown said that behind all her many great, historic achievements lay "the story of a woman who broke the mould and never give up."
Her leadership, at a vital time, undoubtedly helped drive the demand for peace and reconciliation in Ireland.
Tánaiste Eamon Gilmore
Eugene McGlone, Irish Congress of Trade Unions President, said her track record in the field of women's and human rights was unequalled.
"Her work in promoting the cause of labour and social justice in Northern Ireland was known world-wide."
Ms McCormack was also founder and adviser to the pioneering organisation Participation and the Practice of Rights organisation (PPR), which supports local disadvantaged communities.
Nicola Browne, Director of Policy at PPR, said: "We are devastated by the death of Inez, our founder, adviser and dear friend. Inez believed in, and struggled for, the dignity of people at the hardest end of society, and this conviction fuelled her life's work.
"In the trade union movement she supported the lowest paid women cleaners, and as a human rights campaigner, Inez used her formidable intelligence and warmth to bring about change on the ground for communities and groups that needed it most."
Sinn Féin President Gerry Adams said: "Inez McCormack was a fearless opponent of injustice and a determined champion of civil rights, equality, women's and workers rights, and fair employment.
"She was a passionate and articulate campaigner who helped place equality at the heart of the Good Friday Agreement," he added,
SDLP Foyle MP Mark Durkan said: "As an organiser and as an advocate she championed the right of those serving others for lower pay than they deserved."
He continued: "Her contribution to public life went beyond her primary role as a worker's defender as she helped to benchmark the values, principles and protections that were needed for a fair and stable society."
Meryl Streep portrayed Mrs McCormack in the New York theatre production of the documentary play, SEVEN, in 2010.