The deal was announced Wednesday night.
The 31-year-old Montador is set to become an unrestricted free agent Friday. Until then, Chicago has exclusive negotiating rights.
Montador had a career-high 21 assists and 26 points and led the Sabres with a career-best plus-16 rating in 73 games last season.
A Vancouver native, Montador has 28 goals, 89 assists and 762 penalty minutes over parts of nine seasons with the Calgary Flames (2001-06), Florida Panthers (2005-08), Anaheim Ducks (2008-09), Boston Bruins (2009) and Sabres (2009-11).