"My time at Portsmouth has been great for my development, but this is an exciting new challenge for me to push on in my career."
Pulis added: "Asmir is someone we have been tracking for some time and we believe that potentially he is the best young goalkeeper in the country.
"It was important we brought in another goalkeeper because we were a bit exposed in that department. Most clubs in the Premier League have three experienced keepers, but we had managed with just the two for a long time.
"Now Asmir's arrival will provide the extra cover we need and it will also create good competition for places."
The Bosnian's departure is a fresh blow for Pompey, the Premier League's bottom side, who have debts of £60m.
All season, they have been plagued by financial trouble and boardroom upheaval.
They have failed to pay their players on time several occasions, are the subject of a winding-up petition and legal action from former player Sol Campbell, and have only recently had a transfer embargo lifted.
Chief executive Peter Storrie has also revealed transfer deals are going on behind his back, and admitted he and manager Avram Grant both have good reason to walk away from the club, but they would not as "neither of us are quitters."
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