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The 27-year-old spent the second half of last season on loan at Palace, helping the south London club avoid relegation, after falling out of favour with Liverpool manager Jurgen Klopp.
He has signed a four-year contract and is reported to have cost Palace £26 million ($33.6 million, 28.2 million euros).
“I am really happy to be here because I have some friends here,” Sakho said in comments published on the Palace website.
“I loved the challenge last year; it was difficult but beautiful and it’s why this summer I thought that Palace was the best choice.
“I am really excited about playing for the Palace fans again, but in football the past is the past and you need to think about today and tomorrow.
“Last year we did a good job and we need to prove that again and have a good objective. If we put all of our power together, we will have a great season.”
Sakho joined Liverpool from Paris Saint-Germain in September 2013 and became a central figure in the team that narrowly missed out on the Premier League title under Brendan Rodgers in 2013-14.
But he was unable to hold down a first-team place the following season and then fell foul of Klopp due to disciplinary issues after the German’s arrival in October 2015.
He joined Palace on loan in January this year and impressed in his first four months before succumbing to a knee injury that ended his campaign.
Sakho tested positive for a fat-burning drug in April 2016 and missed Euro 2016, but UEFA subsequently revealed the substance he had taken was not on their list of prohibited substances.
He has not played for France since and with the World Cup in Russia coming up at the end of the season, he will hope his return to Palace helps him force his way back into the plans of national coach Didier Deschamps.
Palace have made a poor start to life under new manager Frank de Boer, losing their first three league games.
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