"It feels incredible. It has been a long couple of weeks, but to finally get it over the line is an incredible feeling," Dorrans told the Rangers website (www.rangers.co.uk)
"I just can't wait to get the boots on and get started."
The 54-times Scottish champions suffered a humiliating loss to Luxembourg's Progres Niederkorn on Tuesday and were eliminated from the Europa League.
(Reporting by Aditi Prakash in Bengaluru, editing by Nick Mulvenney)
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