The American midfielder had been searching for a new club since Rangers was relegated to the third division due to economic troubles.
The American midfielder was disenchanted with the possibility of continuing his Rangers career in the dregs of the Scottish pyramid, instead opting to join the Swedish champion.
Bedoya will thus have the opportunity to participate in Champions League football, as The Reds will continue their qualifying run by facing Bedoya's old foe Celtic in the pre-group play-off as early as August 21.
The move ends speculation that Bedoya was looking to leave the Scottish giants, as Rangers manager Ally McCoist had said earlier this week that Alejandro as well as American teammate Maurice Edu were looking for new clubs.
"I think Ale Bedoya is away today to Helsingborgs. We may yet lose more players so we will need to bring more in," said the veteran manager at a press conference today.
Bedoya will begin his second stint in Sweden, having previously suited up for Orebro before joining Rangers.