Sakho was briefly suspended in March 2016 after he tested positive for a fat-burning substance called higenamine following a Europa League game for Liverpool against Manchester United.
The ban led to his absence from the squad for Liverpool's Europa League final against Sevilla.
He claimed the suspension also cost him a place in Didier Deschamps’ group for France's Euro 2016 campaign.
Sakho was ultimately cleared in July 2016 by the disciplinary panel at European football’s ruling body Uefa.
It found that higenamine was not on Wada's banned list and the agency's own laboratories were unsure about its status.
“I feel happy, happy for my family, happy for all my friends, for all the people who were around me during this tough year,” said Sakho outside the high court in London.
The 30-year-old issued a tweet after the court's decision saying his dispute with Wada was closed and he accepted their apology.
"I consider myself vindicated and I look forward to continuing my career," he added.
Sakho sued Wada for defamation after it issued two statements, to the Daily Telegraph in August 2016 and to the Guardian in April 2017, which said he was guilty of taking a prohibited performance-enhancing drug.
Harm
His barrister, Julian Santos, said: “The defamatory allegations were republished by a very large number of media organisations to many millions of readers, causing very serious harm to Mr Sakho's reputation.
"Wada has apologised and agreed to pay a substantial sum by way of compensation and not to repeat the allegations.”
Guy Vassall-Adams, representing Wada, said: "Wada accepts that it should not have made the defamatory allegations it did ... given that Mr Sakho had been acquitted by Uefa.
"Wada accepts that Mr Sakho did not breach the Uefa anti-doping regulations, did not cheat, had no intention of gaining any advantage and acted in good faith.”
Sakho, who joined Crystal Palace in 2017 added: “It is not easy when you are a professional footballer or athlete. This is the worst thing you can be accused of, doping.”
