The 24-year-old had been strongly linked with a move away from the French capital but a suspended two-month prison sentence he received last year having been found guilty of assault complicated matters surrounding a work permit.
Aurier missed PSG's Champions League trip to Arsenal last November as British authorities barred the Ivorian international from entering the United Kingdom after he was convicted for assaulting a police officer.
The defender, who can operate at right-back as well as centre-back, is expected to sign a five-year contract with Tottenham in a deal worth 25 million euros ($29.7 million), according to French daily L'Equipe.
Aurier would become Tottenham's fourth recruit in the past week following a club-record deal for Ajax defender Davinson Sanchez, goalkeeper Paulo Gazzanigga from Southampton and Argentinian youngster Juan Foyth from Estudiantes earlier on Wednesday.
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He would replace England full-back Kyle Walker, who was sold to Manchester City for £50 million in July.
Aurier has yet to play for PSG this season following the arrival of Brazilian international Dani Alves from Juventus.