Storeys, based in the northeast of England, trades from 30 outlets and its sales reached£32.8 million in the year to March 3 last year.
Storeys will sell for an initial price of£18.5 million, but a potential extra£1 million could be added to the deal.
Carpetright chairman and chief executive Lord Harris of Peckham said: 'I am delighted that we have been able to acquire Storeys. The business has a strong heritage and presence in the Northeast - an area where we are not well represented at present. We see significant opportunities to develop the business and deliver attractive returns to our shareholders. Storeys will continue to trade as a stand alone operation under its existing retail brand.'
Peckham added that Carperight European chief executive John Kitching will be appointed chief executive of Storeys. He will work with the existing management team, including Simon Heptinstall, grandson of the original founder.
Carpetright operates from 510 stores in the UK and Ireland and 109 stores across Europe.