Her husband Mark Barrott, aged 54, is wanted as a suspect for her murder.
A Leeds Teaching Hospitals NHS Trust spokesperson said her death had come as "a shock to her colleagues" and revealed that she had worked as a staff nurse in Leeds since 1996.
Paying tribute, the Leeds Teaching Hospitals NHS Trust spokesperson said: “It is with great sadness that we have heard about the sudden and unexpected passing of Eileen Barrott.
"She will be sadly missed by all her friends and colleagues across the Trust.
"Eileen worked as a staff nurse across a number of departments since joining the Trust in 1996.
“This has been a shock to her colleagues and we’re doing all we can to support them at this difficult time.”
Mr Barrott was seen on CCTV travelling to Edinburgh from Leeds Station on Sunday afternoon.
He is known to have arrived in Edinburgh.
He was last seen on CCTV in Huntly Street in the city centre at 9.16pm on Sunday.
Senior Investigating Officer, Detective Chief Inspector Vanessa Rolfe said: “We are continuing to carry out extensive enquiries to locate Mark Barrott as a suspect for his wife Eileen’s murder.
“We are liaising closely with our colleagues from Police Scotland who have established the most recent sighting of Mr Barrott on CCTV in Aberdeen city centre on Sunday night.
“We are keen to hear from anyone who has seen him since then or who has any information that could assist in tracing him.
“We continue to advise anyone who does see him not to approach him but to contact police immediately on 999.
“Eileen’s family have been left completely devastated at her death in these circumstances and we are doing everything we can to support them as we progress the investigation.”
A picture of Eileen Barrott was released by her family today.