The Swedish midfielder, 31, was named on the bench for the first time on Saturday for the Gunners' 6-0 hammering by Chelsea after recovering from a back injury.
Kallstrom has now revealed that he was taken aback by Arsenal's interest in him at the start of the year.
"It was bewildering to say the least," he told Sport Expressen. "It went very quickly. Then everyone at Arsenal took care of me very well, it's been great care and rehabilitation.
"Everything has been well managed and I have received good care and rehabilitation. It has gone very well.
"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 return to Premier League action tonight when they entertain Swansea City at the Emirates Stadium.