The deal for the 25-year-old smashes the previous record set when Paul Pogba returned to Manchester United from Juventus for £89m in August 2016.
He will earn 45m euros (£40.7m) a year – 865,000 euros (£782,000) a week – before tax from the initial five-year deal, a total outlay of £400m.
Neymar wore number 11 at Barca with Lionel Messi occupying the 10 shirt, which is the jersey he wears for Brazil’s national team.
Neymar said he has joined “one of the most ambitious clubs in Europe”.
“Paris St-Germain’s ambition attracted me to the club, along with the passion and the energy this brings,” he added.
“I feel ready to take the challenge. From today, I will do everything I can to help my new team-mates.”