Sodje found the net 13 times in 33 matches for Preston North End and Scunthorpe in League 1.
The former Sheffield Wednesday player was hampered by injury during his time at Glanford Park and was released at the end of last season.
Tranmere manager Ronnie Moore said: “I’m pleased to be able to bring Akpo to Tranmere as he’s a player I’ve been looking at for some time".