The Greek can play at centre back and as a right back, giving Rangers some much-needed cover at the back after the Ibrox side loaned out Romanian defender Dorin Goian to Italian Serie B side Spezia.
Argyriou spent the last two seasons with AEK Athens making 11 league appearances and previously played for AEK rivals Panathinaikos.
The 24-year-old becomes Rangers’ seventh signing following the signings of Ian Black, Dean Shiels, Fran Sandaza, Emilson, Kevin Kyle and Sebastien Faure.
Meanwhile one player’s time at Rangers looks to be at an end as want-a-way midfielder Maurice Edu has agreed personal terms with English Premier League side Maurice Edu.
The 26-year-old is leaving Ibrox for an undisclosed fee, after stating is desire to move away from the club following their emotion to the Scottish Third Division. The American’s move is subject to passing a medical over the weekend and then a work permit being granted before the move can become official.
He will join former Rangers team-mate Jamie Ness at the Britannia Stadium .