The 33-year-old midfielder has not played a professional game in over two years after falling out of love with the game, but is back on familiar territory at Prenton Park.
The ex-Wales international, who lists West Brom, Cardiff and Wigan among his former employers, made over 150 appearances for Rovers after beginning his career there in 1998 and has been back on the Wirral training with Ronnie Moore's side.
Moore was delighted to seal the signature of a player he called 'one of the most talented players the club has ever had'.
"He fell out of love with the game and hasn't played for two years but he came in at the start of July and met us and said he wanted to start playing again," Moore said.
"His attitude has been first class since he has been back and he certainly hasn't lost any of his ability.
"He has trained really well over the last month and has been getting fitter and fitter. When he's fully fit I believe in Jason we will have one of the best players in League One."
Koumas played in the pre-season friendly against Wrexham last weekend but, given his lengthy time away from football, Moore is uncertain if he will feature against Walsall on Saturday.