The settlement will see Dr Polkey's insurers paying a six-figure compensation sum plus legal costs to Helen Brice, of Northstead, and her eight-year-old daughter.
The settlement was made without any admission of liability from Dr Polkey, who is based at Dane's Dyke surgery in Newby.
The agreement between the parties follows a long-running court battle which was due to go to trial at Leeds County Court.
Mrs Brice, 39, who works as a physiotherapist, said: "It's been pretty horrendous. It's hard enough losing someone, but having to fight for answers and justice has been difficult.
"It's come to an end now, but it's a shame it didn't get its day in court."
Dr Nick Whelan, senior partner at Scarborough Medical Group, which runs Dane's Dyke surgery, said: "We genuinely regret we're unable to comment in detail on this case.
"Neither Dr Polkey, her colleagues or her expert advisors consider her liable.
"Dr Polkey had and continues to have our full confidence. Our sympathies are extended to all involved in this case."
Mrs Brice's husband died on April 13 2004 from a brain haemorrhage. He worked as a mechanical engineering supervisor at Greaves in Scarborough.
It was alleged that Dr Polkey failed to diagnose this condition or to send Mr Brice for furtherinvestigations at a consultation on March 31 2004.
After he was admitted to Scarborough Hospital on April 10 2004, it was found that he had suffered a massive brain haemorrhage and he remained in a coma until his death three days later.
Medical notes prepared by Dr Polkey referred to Mr Brice attending with a "sudden onset" headache which experts for Mrs Brice argued were a "red flag symptom" which should have triggered an immediate and urgent referral on to a specialist hospital for further investigations.
The claimants' neurosurgical expert was of the view that if Mr Brice had been referred on to hospital by Dr Polkey on March 31, this would have led to further investigations which would have diagnosed his subarachnoid haemorrhage and allowed for treatment to be given which could have saved his life.
Both GP experts – for the claimant and defendant – agreed that Dr Polkey's examination of Mr Brice did not comply with the standards of examination one would expect from a reasonably competent GP – noting that there was no evidence that she checked pulse, temperature and blood pressure or carried out a central nervous system examination or laid Mr Brice down to check for neck stiffness.
Following a denial of liability by Dr Polkey, court proceedings were issued in August 2007 and had been scheduled to come to Leeds County Court for a three-day trial this month.
Stuart Hanley, Partner at Langleys, said: "Mrs Brice is pleased that after a long battle compensation has been secured for herself and her daughter.
"While noting the lack of admission of liability by Dr Polkey, she hopes that lessons will be learned which will prevent another family going through a similar incident in the future."