The former Under-21 international has penned a two-year contract after impressing during a two-week trial.
The 24-year-old found himself without a club this summer after being released by AEK Athens.
Argyriou spent the last two seasons with the Greek giants, but found himself restricted to just 11 appearances.
He becomes the seventh summer arrival at Rangers, with the Old Firm outfit in the process of rebuilding after slipping into liquidation.
"Rangers have completed a deal for Greek defender Anestis Argyriou," read a statement on the club's official website.
"He has done enough to convince Ally McCoist that he is worthy of a contract and he has successfully completed a medical and signed a two-year contract.
"International clearance has come through for Argyriou so he is free to be involved in the third league match of the season if McCoist wants him."
Argyriou played the full 90 minutes in Sunday's 1-1 draw at Berwick in the Scottish Third Division.