The brands have had their own concession stall in London's Selfridges department store since September.
The new shops are due to open on Carnaby Street in February next year.
Cheap Monday, a jeans retailer, and Monki, a quirky brand for young women, were bought by H&M in 2008.
In July this year, H&M entered a partnership with David Beckham to sell his underwear range exclusively in its 1,800 shops worldwide.
The Swedish group has formed several other celebrity partnerships and has created ranges with Stella McCartney, Madonna and Chanel's Karl Lagerfeld.
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