Aurier, who replaces Kyle Waker in the Spurs squad following his exit to Manchester City earlier this summer, has agreed a five-year deal with the north London club.
The biggest complication in the deal had been organising a work permit for Aurier, who received a suspended prison sentence after assaulting a police officer in Paris last year.
As a result, the player had been prevented from even entering the United Kingdom. But he was eventually granted the paperwork and given Home Office clearance on Wednesday.
Speaking to the club's official website, he said: “This is a huge and exciting opportunity at a massive football club and I am determined to prove myself as a professional both on and off the pitch.
"This is a fresh start for me and I will do everything to make the Spurs fanbase, which is huge and diverse, proud of me. The fans are the most important people at any club and I am looking forward to showing them and everyone at Spurs the real Serge Aurier.”
Aurier is the latest defensive acquisition for Spurs since last season after existing deals for South American duo Davinson Sanchez and Juan Foyth from Ajax and Estudiantes respectively.
Kevin Wimmer left the club for Stoke earlier this week as he seeks more playing time.
Having started his professional career with Lens after moving to France as a 13-year-old, Aurier rose to prominence during his time with Toulouse and joined PSG, initially on loan, in 2014.
He won domestic trebles in each of his first two seasons in the capital, adding further cup and league cup honours in 2016/17 as Monaco wrestled the Ligue 1 title away.