Barclay ruptured his Achilles playing for former club Scarlets against Glasgow in last season’s Guinness Pro14 semi-final at Scotstoun.
He had already agreed to rejoin Edinburgh but has not been able to play for the capital club this season due to the injury.
But the back-row forward is back in training and has been added to the Edinburgh squad along with centre Mark Bennett.
Richard Cockerill’s side host Munster in the Champions Cup quarter-final at BT Murrayfield on 30 March.
Under tournament rules, clubs can nominate up to three players for registration to supplement their European squads.
Glasgow Warriors, who face Saracens away in the last eight, have added prop Zander Fagerson, flanker Callum Gibbins and back Kyle Steyn.