The 31-year-old joined the north Londoners on deadline day despite a medical showing the player had a microfracture in his back.
"It was bewildering [joining Arsenal] to say the least," Kallstrom told Sport Expressen. "It went very quickly. It was surprising. It was nothing I had expected. Of course I was surprised.
"I've had a good career, they needed an experienced player and I fit the profile and took the opportunity."
Arsenal will attempt to bounce back from its 6-0 thrashing by Chelsea against Swansea City on Tuesday, a match which could see Kallstrom finally make his debut.
The midfielder says his recovery has gone well and has praised the Arsenal medical staff for their help with his injury.
"Then everyone at Arsenal took care of me very well, it's been great care and rehabilitation,” he said. "Everything has been well managed and I have received good care and rehabilitation. It has gone very well."