The former Liverpool defender was briefly suspended in 2016 after he tested positive for a fat-burning substance called higenamine after a Europa League game against Manchester United in March that year.
Sakho missed the Reds' Europa League final against Sevilla and, he also alleged, a place in France's Euro 2016 squad as a result of his suspension.
The 30-year-old was ultimately cleared in July 2016 by UEFA's disciplinary body, which found that higenamine was not on WADA's banned list and the agency's own laboratories were unsure about its status.
WADA later issued two statements, to the Daily Telegraph in August 2016 and to the Guardian in April 2017, which said Sakho was guilty of taking a prohibited performance-enhancing drug.
Sakho, who joined Palace in 2017, sued WADA for defamation and, at a High Court hearing in London on Wednesday, accepted an apology from the agency and an undisclosed sum in damages.
"I consider myself innocent," Sakho said in a statement.
"To officially receive the apology from WADA was for me something essential in order to be able to definitively turn the page."
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".
He said: "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."
Speaking outside court, Sakho said: "I feel happy, happy for my family, happy for all my friends, for all the people who were around me during this tough year because it is not easy when you are a professional footballer or athlete.
"This is the worst thing you can be accused of, doping."