The 17-year-old made a lasting impression on the PSV coaching staff during a trial in May.
The teenager is seen as a future international star for Denmark and PSV were keen to bring him in from B93.
Jakobsen has signed a three-year deal but it is not yet known if he will join Guus Hiddink`s first-team squad or be farmed out on loan.
In other news, PSV have sanctioned the season-long loan of teenage forward Nyron Wau to Helmond Sport.
The 19-year-old is rated quite highly at the Philips Stadion and the Eredivisie champions are keen for him to gain some competitive experience.
Wau has made just one appearance for PSV`s first-team, but it was a positive experience as he won a penalty during the victory over PAOK in the Uefa Cup in December 2001.
