The fee, equivalent to Neymar's buyout clause, shatters the existing record of €105m, set last year by Paul Pogba.
In the late afternoon Barcelona confirmed they had accepted the bid and a transfer of a player they bought four years ago looked certain.
Neymar's world record move from Barcelona to Paris Saint-Germain is facing one final awkward hurdle before completion. And the biggest challenge, what most motivated me to join my new teammates is to help the club to conquer the titles that their fans want.
And PSG bigwig Nasser Al-Khelaifi has expressed his delight at getting the mega deal done.
He is confident that the Brazilian will make a difference to the Parisians this season.
The player is now due to arrive in Paris on Friday, according to airport sources in the French capital, to complete the deal.
UEFA, European football's governing body, told Reuters on Wednesday that had been no complaint received so far about PSG in this respect, adding that it would not block any potential deal in advance.
The French football league LFP said on Thursday it did not understand why the Spanish league rejected the payment.
"Neymar Jr is today one of the very best players in world football".
"And I think that's the problem".
"I think he is expensive in the fact that now you are going to have more players at £100 million, you are going have more players at £80 million and more players at £60 million".
"Today, with the arrival of Neymar Jr, I am convinced that we will get closer, with the faithful and fervent support of our fans, the realisation of our greatest dreams".
"The Club will pass on to UEFA the details of the above operation so that they can determine the disciplinary responsibilities that may arise from this case", continued the Barca statement.
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