A regularly guest on BBC Radio 4 panel shows The News Quiz and I'm Sorry I Haven't A Clue, has died from cancer aged 57, his publicist has said.
In a statement, Hardy's publicist Amana Emery said he was with his daughter and wife when he died and his friends and family were "immensely sad".
"He retained to the end the principles that guided his life; trying to make the world more humane, and to be wonderfully funny," Ms Emery said.
"He will be enormously missed by so many, who were inspired by him and who laughed with him.
Jack Dee, who worked with Hardy on Channel 4 sketch show Jack and Jeremy's Real Lives and I'm Sorry I Haven't A Clue, tweeted that Hardy was "ground-breakingly brilliant, off the register funny, compassionate and caring".
Fellow comedian David Baddiel called his death simply "a great loss to comedy".
Born in Farnborough, Hampshire, in 1961, Hardy studied at the University of Southampton before turning to stand-up comedy in the 1980s, winning the prestigious Perrier Award in 1988.
He was soon noticed by television, beginning his on-screen career in 1986's Now - Something Else, appearing alongside Rory Bremner.
The impressionist posted that Hardy was "unfussy, unshowy, principled, self-deprecating," and "funnier than the lot of us [comedians] put together".
In 1993, he began Jeremy Hardy Speaks to the Nation, a series of comedy lectures for BBC Radio 4, which ran for 10 series.
Like many of his '80s contemporaries, Hardy was an overtly political comic and, as a life-long committed socialist, he railed against the perceived injustices of the Conservative governments of Margaret Thatcher and John Major.
He was also fiercely opposed to the Iraq War begun by the labour government of Tony Blair.
Deputy Labour leader John McDonnell praised Hardy for "courageously supporting campaigns for social justice".
His radical views did not always go down well, however, and he was once booed by members of the audience on Radio Four's Just A Minute for ranting about the Royal Family when asked to talk about "parasites".
In 2004, Burnley Council cancelled one of his shows after he said members and supporters of the British National Party should "be shot" on an episode of his Speaks to the Nation programme.
Hardy was twice married, to American actress and comedian Kit Hollerbach, who appeared alongside him in radio sitcoms and with whom he adopted a daughter, Elizabeth, in 1990.
He is survived by his second wife, film-maker and photographer Katie Barlow.