The Ivory Coast right-back, 24, has signed a five-year contract until 2022.
The deal was held up by work permit complications as a result of Aurier receiving a suspended sentence for assaulting a police officer last year.
"This is a fresh start for me. I am determined to prove myself as a professional both on and off the pitch," said Aurier.
"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 Spurs' fourth summer signing, following the arrivals of goalkeeper Paulo Gazzaniga and centre-backs Juan Foyth and Davinson Sanchez - the latter in a club record £42m deal from Ajax.
He is a direct replacement for Kyle Walker, who was sold to Manchester City in a deal worth up to £50m in July.
Aurier joined PSG from Toulouse - initially on loan - in 2014 and has won two French titles and two French cups.
In addition, he represented the Ivory Coast at the 2014 World Cup and started every game when they won the Africa Cup of Nations in 2015, scoring in the penalty shootout win over Ghana in the final.
While at PSG, he was banned for three European matches after insulting referee Bjorn Kuipers on Facebook.
Then, in March 2016, he was suspended indefinitely after appearing to use homophobic language to insult coach Laurent Blanc and calling team-mate Angel di Maria a "clown" on social media app Periscope.
Aurier, who was ordered to train with the reserve team, later apologised for his "inexcusable" behaviour.
He returned to the PSG side and made 22 league appearances last season, despite being convicted of elbowing a police officer after leaving a nightclub in May 2016.
Aurier was stopped from entering the United Kingdom in November 2016 before PSG's Champions League match against Arsenal as a result of the two-month sentence.