Campoli, 27, had 21 points in 77 games with Ottawa and Chicago last season.
A restricted free agent following the season, Campoli was unable to come to terms with the Blackhawks. He became an unrestricted free agent in late July when Chicago general manager Stan Bowman walked away from a $2.5 million arbitrator's settlement, a formality which was negotiated before Campoli's arbitration hearing once it became clear that a deal wouldn't get done.
The Canadiens are awaiting the return of All-Star defenseman Andrei Markov from a second knee operation in two years. Markov had a setback in his rehabilitation and isn't expected to be ready for the beginning of the regular season.