Elaine Brown, aged 69, from Merseyside, who stayed at the Feathers Hotel on July 31 last year with her husband Graham, died on August 26 after suffering a stroke as a result of contracting the disease.
The hotel voluntarily shut for two months following Mrs Brown's death, and laboratory tests revealed her illness was linked to Legionella bacteria from the hotel plumbing.
Public Health England (PHE) later released details of another former guest who contracted the disease in April 2017, although that guest went on to make a full recovery.
The PHE investigation is ongoing and its formal Outbreak Report is yet to be released.
The Feathers has now made a formal admission of civil liability to the family of Mrs Brown, paving the way for a future financial settlement.
The admission came after the family instructed solicitors from Irwin Mitchell's public health team to investigate the circumstances surrounding Mrs Brown's death, determine whether more could have been done to protect her, and whether guests should have been allowed to stay at the hotel given the outbreak earlier in the year.
Jatinder Paul, an associate solicitor at Irwin Mitchell who is representing Mrs Brown's family, said: "It is more than six months since Elaine passed away and her family remain understandably devastated and angry at their avoidable loss.
"Whilst we welcome the admission of liability by the hotel as a positive step forward for the family in this legal action, ultimately the hotel’s decision to take responsibility for its failures cannot turn the time back and Graham has lost his dear wife."
The 40-bedroom hotel reopened in November after remedial work was carried out, and samples came back clear. Shropshire Council also opened a formal investigation.
The Feathers was put up for sale in January for more than £2.6 million.