The 27-year-old switches to Signal Iduna Park for a fee reported between €20 million and €22 million, with Borussia Dortmund forced into swift action given the release clause's limited remaining window.
Veerman has signed a contract running until 2031, and is expected to reshuffle the cards in Dortmund's central midfield, with a departure for Marcel Sabitzer, 32, now considered a real possibility.
For the Dutchman, who has already earned 16 caps for the Netherlands, the move represents his first step into football outside his home country.
Speaking about his new club, Veerman said he was proud to complete the switch.
"Borussia Dortmund is a big club in Europe and I'm proud to now be part of this club. I'm really excited to be here and want to celebrate success together with BVB."
Dortmund sporting director Ole Book was equally warm in his welcome for the new arrival.
"Joey is a really great footballer, who has a lot of creativity, technique and vision.
"He has shown at PSV Eindhoven and with the Dutch national team that he can consistently perform at the top level. We're delighted that he'll be bringing his qualities to our style of play in the future."
Veerman made 198 appearances for PSV since joining in 2022, scoring 31 goals and providing 67 assists, and won three Eredivisie titles and two Dutch Cups during his time in Eindhoven.
His arrival follows Dortmund's signing of Giannis Konstantelias from PAOK Saloniki a day earlier, with the club effectively splitting the transfer budget it had originally set aside for Said El Mala across the two deals after missing out on the Köln winger.