In a statement, the leader of the Liberal Democrats Sir Ed Davey said that news of her death was “heartbreaking”.
He described her as “an inspiration to millions, a Liberal lion and a true trailblazer”.
“I feel privileged to have known her, listened to her and worked with her. Like so many others, I will miss her terribly,” he said.
"Political life will be poorer without her intellect, her wisdom and her generosity,” he added.
“Shirley had a limitless empathy only too rare in politics today; she connected with people, cared about their lives, and saw politics as a crucial tool to change lives for the better.”
The party said Baroness Williams had passed away peacefully in the early hours of this morning.
She was one of the so-called “Gang of Four”, a group of disenchanted Labour politicians who became the founders of the breakaway Social Democratic Party.
Before that she had served as education secretary in the years before Margaret Thatcher came to power.
Former prime minister Tony Blair also paid tribute to her, saying that even after she left Labour she remained a source of inspiration to many in the party.
“Shirley Williams was one of the greatest social democrats of the last century, an immense figure of progressive politics through the decades, consistent in her commitment to equality, to social justice, to liberal social democratic values and to internationalism,” he said.
Commons speaker Sir Lindsay Hoyle described her as “one of a kind”.
“She was a trailblazer for women and education, one of the first women to sit in cabinet and the only female member of the ‘Gang of Four’.
“Without doubt, she was one of a kind, and a character we all shall miss,” he said.
Shirley Vivian Teresa Brittain Williams was born on 27 July 1930, the daughter of Vera Brittain, the high-profile feminist and author of Testament of Youth.
She entered parliament as MP for Hitchin in 1964 and eventually became a cabinet minister.
But disillusioned with Labour’s lurch to the left after the election of Thatcher, she joined with William Rodgers, David Owen and Roy Jenkins to form the SDP, later becoming the party’s first elected MP.
In 1988, after an alliance lasting a few years, the SDP formally merged with the Liberal Party, forming the Social and Liberal Democrats, later to become the Liberal Democrats.
Williams became a life peer in 1993.