The Denmark international has been told by Felix Magath that he will be allowed to move clubs and is looking forward to his proposed transfer to Stadio Olimpico
Kjaer has long been linked with a return to Italy, but it was believed until now that Wolfsburg were keen to hold on to the centre-back.
"Felix Magath has told me that I will be allowed to leave and that I can enter negotiations with other clubs. It was my personal wish to stay at VfL, but I'm also pleased with this outcome," Kjaer said to WAZ.
"A return to Italy can be a done deal any hour now. Roma are a great club. Joining them is a big opportunity for me. I don't have to adapt to new surroundings as I'm already familiar with Italy and Serie A."
Roma see the 22-year-old Kjaer as the perfect replacement for Philippe Mexes, who left the club for AC Milan this summer, and they're willing to pay up to €10 million (£8.7m) for the centre-back.