Murphy, 31, heads to Easter Road on-loan for the remainder of the campaign with the deal becoming permanent at the end of the season.
Murphy arrived at Rangers from English Premiership side Brighton and Hove Albion in January 2018, initially on-loan before the deal became permanent in the summer of that year.
His initial loan spell was successful, scoring five times in 20 appearances, and he made a strong start to life under new manager Steven Gerrard, netting the first goal of his era against Shkupi in the Europa League qualifiers.
A serious knee injury sustained at Kilmarnock in August 2018 left him out of action for over a year. Following his recovery, he joined League One’s Burton Albion on-loan in January 2020.
Rangers Sporting Director, Ross Wilson, commented: “Jamie has been a dedicated professional during his time at Rangers, having worked hard to overcome his unfortunate injury.
“He leaves Rangers with our very best wishes for the future.”