Edjenguele became a free agent at the end of last season after his contract with Greek side Panetolikos expired and Sky Blues boss Andy Thorn has been impressed by what he has seen.
The 25-year-old becomes the second French defender to join Coventry in the space of five days after the arrival of Kevin Malaga.
Thorn told City's official website: "William is a strong, physical presence. He has played at a good level in Greece and we're delighted to have him on board.
"We've had him in for a while now. He's been training with us, he did really well at Hinckley (in an 8-0 pre-season victory on Saturday) and has generally impressed.
"We were aware of what he had to offer and, similar to Kevin Malaga, it was important we tied him down and we've done that, which I'm pleased about."