The 22-year-old has spent 14 years with the Ibrox club after rising through the academy ranks, but has managed just nine appearances since making his first-team debut in 2017.
The midfielder finished the season on loan at Ayr United, and has also had previous loan spells at Raith Rovers, Partick Thistle and Bury.
Posting to Instagram, Barjonas wrote: “So, after 14 years my time at Rangers has come to an end.
“From soccer schools on Sundays to making my first team debut I’ve made so many amazing memories that will stay with me for life.
“To the unbelievable fans who make the club so special I’d like to say thank you for the support.
“To everyone who played a part along the way I will be forever grateful & I wish the club nothing but success in the future.”
Ally McCoist, his former manager at Rangers, added his support, posting: “Very best of luck. Go and flourish.”