Fabric Scandinavien also owns the MTWTFSS Weekday and Sunday Sun brands.
Cheap Monday has around 1,000 wholesale stockists.
The six-store Weekday chain is an urban unisex concept. It will open its first store outside of Sweden this month in Copenhagen, Denmark.
The Monki chain has 12 stores and targets women with own brand fashion.
Fabric Scandinavien is set to hit sales of SEK 400 million (£32.8m) for the financial year 2007/2008.
H&M paid SEK 564m (£46.6m) for a 60% share of the Fabric Scandinavien. The company will be run as a standalone subsidiary within the H&M group.
H&M chief executive Rolf Eriksen said: "We see potential to develop stores and concepts in other markets. By working together we can accelerate the growth further. We can also do it in a more efficient manner by drawing on H&M's experience and knowledge of for example production, logistics and establishment."