He made a try-scoring return to rugby on Saturday for Melrose in the side's RBS Premiership win over Gala at Netherdale, and now moves to the Liberty Stadium to seek game time.
Parker, Welsh qualified through his father, will provide much needed second row cover for the club in the absence of Alun Wyn Jones and James King (international duty), Ian Evans (suspended) and Ryan Jones (injured).
Edinburgh Rugby head coach, Alan Solomons, said: "It's been a tough season for Perry [Parker] who's been out for a long spell with an injured shoulder.
"We have good depth in the second-row, so this is a good opportunity to get valuable game time.
"We wish him all the best in west Wales."
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