The Scottish champions have been strongly linked with a move for the 23-year-old across the past 12 months.
Speculation over the player's future was decided on Tuesday with PSV announcing they had signed the player from Heerenveen on a deal until 2026.
It is understood the transfer was worth more than £5million.
The club's director of football affairs, John de Jong, explained why the player was sought after with PSV managing to get the deal done swiftly since putting an offer in at the weekend.
"We had a lot to do with completing the transfer quickly and we are happy that this was successful,” he said.
"Joey is a multifunctional midfielder who adds creativity to PSV. Given the composition of the selections we thought we could use such a type.
"We have been keeping a close eye on Joey for some time and are convinced that he has not reached his ceiling yet.”
Rangers, alongside the likes of Feyenoord and Atalanta, wanted the player in the summer but Heerenveen stood strong in their valuation of the player.
Veerman, at the time, was eager to move on from Heerenveen and felt the club’s €10million-plus price tag was “crazy”.
This move sees the midfielder joining his boyhood club.
He said: “I am looking forward to playing football at this wonderful club – the number one in the Eredivisie. You have to perform here every week. I was looking for that challenge.”