Although he was limited to just 28 appearances in his final year at United, the Premier League side hoped to extend his deal but were unable to reach an agreement with the Spain international, allowing him to leave for free when his contract expired.
Reports linking Herrera to a switch to PSG emerged in April and intensified once his departure was confirmed the following month.
And the Ligue 1 champions have acted on their interest by luring him to Parc des Princes with a five-year contract.
"Paris Saint-Germain is the greatest club in France. It keeps on improving and competes to win every possible title," he told the club's website.
"I was looking forward to coming to Paris and to wearing those colors. I hope to continue to make history with the club!
"Joining this club is an amazing feeling. I also love the city. Paris is the most beautiful city in the world. I promise three things: work, professionalism and passion. I also promise to improve my French because I think that the language is very important for the team’s communication.”
Herrera is PSG's second signing of the summer, following Pablo Sarabia, who joined from Sevilla in a €20 million deal.
Thomas Tuchel's side have already waved goodbye to Lassana Diarra and Adrien Rabiot, while Leandro Paredes has been linked with a move away despite only joining from Zenit in January.
Meanwhile, he is the second first-team player to leave United this summer, as Antonio Valencia also departed as a free agent, while Ole Gunnar Solskjaer's team have signed Aaron Wan-Bissaka from Crystal Palace and Daniel James from Swansea City thus far.