The 72-year-old died after a short period of illness, his family said.
Tributes have been paid to Lord Martin of Springburn, former speaker of the House of Commons, who died on Sunday.
The 72-year-old died in the early hours after a short illness, his son Paul Martin confirmed.
He said: "He passed away early this morning after a period of short illness.
"He passed away peacefully with his family.
Very sorry to hear of the death of Michael Martin. We first met as organisers in the National Union of Public Employees, campaigning for decent public sector pay and the national minimum wage. Michael loved his community and family, our thoughts are with them at this sad time.
Labour Leader Jeremy Corbyn offered his condolences, saying he was "very sorry" to hear the news.
John Bercow, the current House of Commons Speaker, said: "I'm very sorry to hear this news.
"Michael was a decent, public-spirited man who had a real care and concern for Members, their staff and the staff of the House.
"He was a good campaigner and both passionate about and proud of his roots. He also had a great sense of humour.
"On a personal level, he was always very kind to me – I still remember the lovely letter of congratulations he sent to me after my election as Speaker.
Michael Martin – latterly Lord Martin of Springburn after the Glasgow constituency he represented from 1979 to 2005 – was Speaker from 2000 to 2009.
Although by tradition speakers are elevated to the Lords, the decision to grant Lord Martin's peerage proved controversial, with some speculation the honour should be withheld.
When he was speaker, he was criticised for leading efforts to block the publication of MPs' expenses, and for his handling of the affair once the revelations began.
Lord Martin was succeeded by John Bercow.
Tony Blair said he personally valued Lord Martin for his common sense and "sound political instinct".