PC Claire Stretton, who has been sacked, was family liaison officer to Charles Foulkes and his wife after their son was murdered in 2001.
Solicitor Nick Turner said their three daughters reached an out-of-court settlement with West Mercia Police.
Ms Stretton was claimed to have manipulated Mr Foulkes for Â£100,000.
Mr Foulkes' daughters took legal action against the force after their father died aged 93 in 2011. Mr Turner said the settlement was reached in the summer.
Papers lodged at the High Court last year said the officer, identified as "PC X", met Mr Foulkes and his terminally ill wife Dorothy, of Church Stretton, Shropshire, after the death of their 49-year-old son Colin.
Colin Foulkes was killed by John Latus who beheaded him with an axe.
Charles Foulkes was the sole beneficiary of his son's estate of about Â£180,000, according to the papers.
"Such was the inappropriate manner in which PC X interacted [with Mr Foulkes], his wife referred to PC X with great distress as his 'bit of fluff'," according to the documents.
The family said Ms Stretton took advantage of "his vulnerabilities" and "abused her position of trust" following the death of his son and later wife.
The officer allegedly sent Mr Foulkes texts saying she loved him and that he was "special".  The daughters said their father gave the officer "substantial sums of money and presents" over a 10-year period.
Ms Stretton, who worked for the force in Telford for 26 years, was dismissed last week for gross misconduct.
Det Supt Gary Watson, head of professional standards said: "The misconduct hearing found that the behaviour of the officer fell below the standards we expect from our officers and staff and amounted to a breach of the standards of professional behaviour, namely discreditable conduct and a breach of honesty and integrity."
Mr Turner, of Russell and Co Solicitors of Malvern, Herefordshire, said the family were "relieved that some semblance of justice has been achieved".
"What should have been a situation whereby the family liaison officer appointed by the police brought support, strength and counselling to the family - instead of that their misery was compounded by the totally inappropriate actions of PC Stretton."
A police force paid an undisclosed sum to a grieving family over an officer's "inappropriate relationship" with their elderly father, their solicitor said.