The transfer smashes the previous record set when Manchester United paid €105m to Juventus for Paul Pogba in August 2016.
"Paris Saint-Germain are very pleased to announce the arrival of Neymar Jr," PSG said in a statement on their website.
"The Brazilian attacker signed a five-year contract in the presence of club and player representatives. Neymar Jr is now tied to the club of the capital until June 30, 2022."
Neymar, 25, will earn €45m a year - €865,000 a week - before tax from the initial five-year deal.
Earlier on Thursday, La Liga refused to accept the €222m payment, citing concerns it may violate Uefa's Financial Fair Play (FFP) rules. However, Neymar's representatives instead paid direct to Barca.