The ex-Labour leader said the pair met at former South African president Mr Mandela’s 90th birthday party, at which Rehab singer Winehouse made a joke comparing the anti-apartheid campaigner to her husband, Blake Fielder-Civil.
In an interview with the Guardian’s G2 magazine, Mr Brown said: “The person he (Mr Mandela) most liked was Amy Winehouse.
“She said to him: ‘You and my husband have a lot in common’. “He said, ‘Oh, what is that?’ “She said, ‘You’ve both spent a long time in prison’.”
Mr Mandela was held in the highest esteem across the world for leading South Africa’s transition from white-minority rule in the 1990s after 27 years in jail. He became the country’s first black president and died last year at 95.
Fielder-Civil, a video producer, was 26 when he was sentenced to 27 months in jail back in 2008 after admitting grievous bodily harm and perverting the course of justice in a £200,000 trial-fixing plot aimed at trying to save him from prison.
He and Winehouse were married in 2007 but divorced two years later after a troubled on-off relationship.
Last year, a second inquest into Winehouse’s death confirmed that she died from alcohol poisoning after a drinking binge. The same verdict of misadventure was recorded at a re-hearing of the inquest - after the first was heard by a coroner who did not have the correct qualifications.
The 27-year-old Back To Black star was found dead at her flat in Camden, north London, on July 23, 2011.