Wilson, 19, recently parted company with the Scottish Premier League side and has spent the past week training with Doncaster and O'Driscoll has opted to offer him a contract.
"It all came about because Sean bumped into my old boss Tony Mowbray at a Celtic reserve game and he recommended me to him and said I would be the type of player he would like," Wilson said.
"I have been at Hibs since I was twelve but now need to progress so coming to Rovers will help that. It has been a bit easier because I know Dean (Shiels) but I have enjoyed my time so far."
Source: Team_Talk