The Finland U21 goalkeeper joins from Chelsea on-loan for the entire season. Chelsea have announced Bergstrm has extended his contract to 2025.
"We are bringing in a big and strong goalkeeper who owns his penalty area," says Brommapojkarna sporting director Philip Berglund to the club's website.
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"He has plenty of experience and played an international match for Finland as recently as January."
Bergstrm also said: "It feels great and I'm excited.
"The team moved up to the Allsvenskan before last season, I know that young players get the chance here at the same time as we play attractive football. I was happy when the interest came from BP.
"I haven't played in the Allsvenksan before but I want us to rise in the table and we go into every game to win. I will stop the balls but we will win the games. I will help the team and do my best for us to succeed."