Rangers manager Ally McCoist yesterday revealed the Norwegian midfielder was heading home and Tromso today announced he had signed a three-year contract.
Rangers had offered the 22-year-old a new contract and they say they will be entitled to compensation following his move.
Bendiksen, whose contract had expired, struggled to make an impact after signing for Rangers in August 2007, with his progress hindered by a serious knee injury.
But he scored in a friendly defeat by Hamburg in November and made his first competitive start for the club in a 2-1 win over Dunfermline last month.
Bendiksen made two more substitute appearances, in victories over Hibernian and Inverness, but his heart was set on a return home.
Bendiksen told Tromso’s official website: “I had a very good contract offer from Rangers but I said ‘no thanks’.
“Tromso IL are a good club with ambitions to be even better.
“I aim to play my way to a permanent place in the team and look forward to an exciting season, both at home and not least in the Europa League.”