The non-state-owned Chinese giant, which is listed on the Shanghai Stock Exchange, acquired an 89% stake in the 165-year-old brand's department stores through its Nanjing Cenbest subsidiary.
The deal has been touted as the largest overseas acquisition ever in the retail sector by a Chinese business, with Sanpower now expected to develop the brand in foreign markets.
Its announcement comes after reports last week that Sports Direct tycoon Mike Ashley had bought an 11% stake in the business, which has a number of stores in Scotland, in an attempt to derail the deal with the Chinese.
The company, which went private in 2006, said it did not expect to see any day-to-day changes for the 7300 House of Fraser staff and 12,000 concession employees working across its 60 stores.
Hailing the announcement Don McCarthy, executive chairman of House of Fraser, said it opened an "extremely exciting chapter in the story of House of Fraser".
He added: "The acquisition by Nanjing Cenbest will allow House of Fraser's management team to continue to grow and invest in the business in the UK and Ireland, provide a strong platform from which to expand the brand in international markets and to further develop our multichannel, stores and premium fashion offering."