As revealed in this week's Retail Week, Blow will succeed Dalton Philips, who left to join Canadian supermarket Loblaw.
Both Brown Thomas and Loblaw are owned by Canadian retail tycoon Galen Weston. His retail empire also includes Selfridges and Holt Renfrew.
Blow will start at Brown Thomas in March. He resigned from Harrods last week.
Weston said: 'I am delighted that Nigel has accepted the position. His proven track record and experience in the luxury goods industry make him the ideal person for the job.'