Wijnaldum, 30, has agreed a three-year deal with PSG after he opted against signing a new contract at Anfield. His existing deal expires at the end of June.
The Dutch international's agent met with Barca president Joan Laporta at the end of May, and a medical had been arranged for this week.
However, as first reported by ESPN on Friday, PSG made a late bid to pip Barca in the race for Wijnaldum's signature, whose interest in the midfielder dates back to last summer following the arrival of Ronald Koeman at the Camp Nou.
Sources close to the negotiations said that the Ligue 1 side offered to double the terms agreed with Barca, and a phone call from coach Mauricio Pochettino also helped persuade Wijnaldum to change his mind.
Wijnaldum had also held talks with Bayern. However, the midfielder informed both the German champions and Barcelona last weekend that he had opted to join PSG.
The midfielder, who is preparing for the European Championships with the Netherlands, becomes PSG's first signing of the summer as they look to strengthen after losing the league title to Lille and a semifinal Champions League exit to Manchester City.
In total, the midfielder made 237 appearances for Liverpool, scoring 22 goals, as well as playing a crucial role in ending the club's 30-year Premier League trophy drought last season.
During his five-year stay at Anfield, he also won the Champions League, UEFA Super Cup and the Club World Cup.