BOSTON—The site of the former Filene’s Department Store here is the setting for one of the most notable retail leases in recent Boston history. European fashion retailer Primark is taking a total of 112,000 square feet at the eight-story Burnham Building, adjacent to Millennium Partners’ Millennium Tower now under construction.

Primark has signed to a long-term lease on four floors in the century-old Burnham Building, of which 70,000 square feet will be selling space. The deal follows recent leases to Havas Media/Arnold Worldwide and Roche Bros. market at the property.

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