The national and regional sales for the two stations, which are based in Manchester and Newcastle, will continue to be handled by GCap.
The acquisition makes GMG the fourth-largest radio group and brings its portfolio of regional stations to seven. The group also owns the Smooth FM stations, formerly known a Jazz FM, and the Real Radio brand.
It is unclear whether GMG plans to rebrand Century as Real Radio – a GMG spokeswoman says the stations will be reviewed after they have been integrated into the group.
John Myers, chief executive of GMG Radio, says: "There are two very good stations, with great people and in areas of the UK we know well. It gives us increased scale and consolidates our determination to be a major force in radio."
Myers is a former managing director of the Century Radio.