The 72-year-old died on Sunday morning 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.
“We would be grateful for our privacy to be respected at this difficult time.”
Michael Martin - latterly Lord Martin of Springburn after the Glasgow constituency he represented from 1979 to 2005 - was Speaker from 2000 to 2009.
In October that year, the former Labour MP joined his predecessor as speaker, Baroness Boothroyd, on the crossbenches.
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.
He was the first Commons speaker to be forced to resign in 300 years.
Lord Martin was succeeded by John Bercow.