The 27-year-old left-sided defender is set to undergo a medical on Monday. Sosa, who played 20 times on loan at Torino last season, is expected to provide strong competition for Tyrick Mitchell at left wing-back, though he is also capable of operating on the opposite flank.
Sosa's move comes after he was reportedly told by new Ajax manager John Heitinga that he was not part of the club's future plans, despite having three years left on his contract.
A veteran of Croatia's 2022 World Cup squad that reached the semi-finals, Sosa brings international pedigree and versatility to Selhurst Park.
His arrival addresses a vacancy left by Ben Chilwell, who joined on loan in January but has since returned to Chelsea.
Palace have also added Argentina goalkeeper Walter Benítez on a free transfer from PSV Eindhoven.
Meanwhile, the club remain in talks with Sporting Lisbon over a potential 45-million-pound deal for Ivorian centre-back Ousmane Diomande.
That pursuit may hinge on the future of Marc Guehi, with Liverpool currently leading the race to sign the England international, whose contract expires next summer.