The centre-back, having long agreed personal terms with the Eagles, waited on the clubs to reach a consensus over his fee.
Frank de Boer’s side had three previous approaches batted away for the Frenchman, who was their priority rearguard target in the window, but common ground was found on deadline day to conclude a transfer that suits all parties.
Despite the Reds ultimately settling for £4m less than their valuation, they have solved a problem that has needed to be fixed since last summer.
Sakho fell out with Jurgen Klopp having breached club rules thrice during their pre-season camp in California while nursing an Achilles problem.
His triple fault was preceded by a lengthy battle against a UEFA doping charge, which he was cleared of, but he had erred by taking a substance without consulting the Reds’ medical staff as per contractual obligations.
And that was followed by a Snapchat rant in September that ultimately spelt the end of any sort of redemption at Anfield.
Sakho has not played for Liverpool since April 20, 2016 but can now close that chapter and hope to thrive at Palace, where he was influential on loan for the second half of last season.
The 27-year-old swapped Paris Saint-Germain for Anfield in September 2013 for £15m, scoring three goals in 80 appearances.