Storch has an industry reputation for enlivening flagging brands and he replaces John Eyler, who left in July last year after the company's US$6.6bn move into private hands.
Storch joined Target in 1993 and was vice-chairman from 2001 to 2005, with responsibilities including technology and financial services, as well as the internet division. He also led the turnaround at the retailer's Marshall Field's business and was widely seen as the potential successor to Target chief executive Robert Ulrich.
Toys R Us interim chief executive Rick Markee will continue in an executive capacity as vice-chairman of the company and president of the Babies R Us division.
Toys R Us is owned by an investment consortium that includes real estate developer Vornado Realty Trust, as well as private equity firms Kohlberg Kravis Roberts & Company and Bain Capital Partners.
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