Saks also said that chairman and chief executive Stephen Sadove and president and chief merchant Ronald Frasch are set to leave the company once it is acquired by Hudson’s Bay
The $2.4bn (£1.5bn) deal, announced in July, has been approved by each company's board and is expected to close before the end of the year. The closing is subject to the approval of Saks' shareholders, among other conditions.
McKee joined upmarket retailer Harrods in 1999 and has been chief merchant since 2011. She has been on the Harrods board since 2005.
Harrods has been owned by Qatar Holding since 2010, when it paid £1.5bn to buy the shop from Mohammed al-Fayed.
Hudson’s Bay is creating an office of the chairman, consisting of chief executive officer Richard Baker and chief operating officer Donald Watros.