The 200,000 ft2 store, in Glasgow's Merchant City district, is due to open in 2007.
Ito is one of the world's most celebrated architects but until this summer, when he designed a temporary pavilion at the Serpentine Gallery in London's Kensington Gardens, he had never built in the UK.
Radice is hailed as the man who turned Selfridges' fortunes around, partly by appointing cutting-edge architects to work on new and existing stores. Designers Ron Arad and David Adjaye have been involved in the London and Manchester stores, and Future Systems' design for a Birmingham store – clad in aluminium discs – is on site.
Future Systems' Amanda Levete said: "He's been an absolutely incredible client. He's put in place a very clear [building] strategy for Selfridges to follow in future." She added that Radice may adopt a similar strategy at M&S: "I can't imagine that he wouldn't get involved in new building projects," she said.