First Minister of Wales and Welsh Labour leader Mark Drakeford said Flynn was a “giant of the Welsh Labour movement”.
He added: “Today’s news will be a source of great sadness to all those who knew him.
“He was one of the most effective communicators of his generation – inside the House of Commons and outside. But it was Paul’s willingness to speak up for causes beyond the political mainstream which marked him out as a politician of real courage and integrity.
“I first met him more than 35 years ago, and it has been a privilege to have worked with him, in the run-up to the devolution era and beyond.”
Jo Stevens, Labour MP for Cardiff Central, described Flynn as a “kind, principled, fascinating man”.
She tweeted: “So very sad to hear that my lovely colleague Paul Flynn MP has died. A kind, principled, fascinating man who was devoted to his constituents constituency. Sending deepest sympathy to Sam, their family to all our comrades in @nptwestlab”.
Flynn, who was a strong advocate for the medicinal use of cannabis, announced in October that he intended to stand down as an MP due to health reasons.
He said at the time: “It’s been a great, wonderful, rich experience. I lasted 31 years.”