Bedoya joined the Ibrox club from Orebro last summer but struggled to hold down a regular first-team place.
The US international was likely to feature more following Rangers' demotion to the third division, but has opted not to transfer his contract to the newco club.
"Hard decisions need made! I've decided to move on but am extremely grateful at opportunity to have played at Rangers! Thanks for support!" Bedoya wrote on Twitter.
"Looking forward to joining up with my new team-mates at Helsingborg tomorrow for my first training session!"
Bedoya, 25, has made 13 appearances for the United States since making his debut in 2010.