The board of Carrefour
Board members took the decision at a meeting on Sunday evening, the source said, but gave no further details.
Plassat, 62, head of private-equity backed retailer Vivarte, replaces Lars Olofsson, who had been living on borrowed time after a string of profit warnings that hammered Carrefour shares down 43 percent over the past year.
Carrefour declined to comment.
Sources close to the matter told Reuters last week that Plassat was close to finalising talks to take the helm of Carrefour.
Olofsson, a former marketing executive from Swiss food giant Nestle
His tenure as chief executive has been marred by a procession of poor trading results, management defections and strategic U-turns, including a failed merger in Brazil, as well as doubts over his flagship plan to revive Carrefour's ailing hypermarkets.
The appointment of Plassat should be viewed as a big win for Carrefour. He is a well-seasoned retail executive with the non-food experience that Carrefour so vitally needs to turn around its hypermarket division, said Natalie Berg, director of global research at Planet Retail.
Plassat spent 14 years at French retailer Casino and two years at Carrefour Spain before heading in 2000 to Vivarte, of which he is also a shareholder.
Speculation that Plassat's arrival at Carrefour was imminent lifted the stock by 8 percent on January 26.
The choice of Plassat, a strong-willed Frenchman with a solid track record for restructuring companies, reflects a push for a turnaround by Carrefour's top shareholders, Blue Capital, an alliance of U.S. private equity fund Colony Capital and Bernard Arnault, France's richest man.
The duo, which bought its Carrefour shares at over 40 euros, together owns 16 percent of the capital of Carrefour and sits on hefty paper losses fom their 2007 investment.
Today, Carrefour shares are down 24 percent since Olofsson took over in January 2009.
(Reporting by Pascale Denis, Dominique Vidalon)