The Wanderers officially announced the 33-year-old's departure on Friday, who was last in action for the club in their 1-0 home loss to Glory which sealed the fate of German coach Markus Babbel at the weekend.
Elrich made 27 appearances last season after returning to Wanderland from Adelaide United, where he spent over four years for 103 A-League appearances.
Though he has started two of Wanderers’ last three games, Elrich has made just five appearances this season with injury setbacks and the emergence of youngster Tate Russell limiting his game time.
Glory coach Tony Popovic is in the process of beefing up his squad for the looming AFC Champions League campaign, and the 33-year-old right-back is set to add extra depth.
And the Wanderers have not stood in the way of a move west, with Elrich due to come off contract at season’s end.
The former Newcastle Jets flier will become Popovic’s second signing in a week following the arrival of midfielder Vince Lia from Adelaide United and will provide extra cover following the long term injury loss of Dino Djublic.
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