MrCooper, 69, is understood to have fallen ill and died before his wife, 63, passed away just hours later.
They were staying at the Steigenberger Aqua Magic Hotel in the Red Sea resort. An investigation is under way and Cook has said all 301 of its guests there will be removed and offered alternative accommodation, or flights home.
MrsCooper, a Thomas Cook employee who worked at the operator’s Chancery Walk branch in Burnley, has been described as a “loyal and long-serving” colleague. The branch was shut on Thursday as a mark of respect.
Carol MacKenzie, Cook’s head of customer welfare, flew out to Hurghada on Thursday to support the Cooper family.
It is believed the couple were holidaying with daughter Kelly Ormerod and their grandchildren.
In a statement, Thomas Cook UK chief Ingo Burmester said: “We are deeply saddened by the deaths of two of our customers while on holiday in Hurghada in Egypt, one of whom was a loyal and long-serving member of our Thomas Cook family.
"Our focus is on fully supporting their loved ones. We are urgently investigating with the hotel and supporting the local authorities.”
A Foreign Office spokesperson said: "We are supporting the family of a British couple who died in Hurghada, Egypt, and we are in contact with the local tour operator."