Madonna was not at London's High Court for the settlement
Madonna has accepted damages from the Mail on Sunday after it breached her privacy and copyright by printing photos of her wedding to Guy Ritchie.
Last year, a judge in London found in her favour over the paper's publication of 11 photos of the 2000 wedding.
He heard they were "surreptitiously" copied by an interior designer working at her Beverly Hills home.
The singer, 51, will donate the substantial undisclosed damages to her Raising Malawi charity.
Madonna, who was not at London's High Court on Tuesday for the settlement, had been seeking more than £5m in damages in her action against Associated Newspapers.
The Mail on Sunday, which admitted wrongdoing, had paid £5,000 for the images of the wedding which took place at Skibo Castle in Scotland on 22 December 2000.
The pictures were published on 19 October last year, days after the singer announced she and film director Ritchie would be divorcing.
Prior to that day, no pictures of the wedding had ever been published.
The singer's solicitor, John Kelly, said she had gone to great lengths to ensure the wedding was kept private and had chosen not to sell pictures to the media.
Madonna and Guy Ritchie were granted a divorce last November
"It was far more important to the claimant that the privacy of the occasion was maintained," he added.
A selection of pictures taken by her friend, fashion photographer Jean-Baptiste Mondino, were in an album which she kept securely at her Beverly Hills home.
At least 27 photos from the album were copied by an interior designer working at her home in 2003 before they were offered to the Mail on Sunday in 2008.
Mr Kelly said the paper had destroyed all its copies of the photographs and had agreed to pay Madonna damages and legal costs.
Solicitor Niri Shan, acting for Associated Newspapers, offered its apologies to the singer and her family for invading her privacy and infringing her copyright.
Madonna and Ritchie were granted a divorce at the High Court on 21 November last year.