He said Dr Ubani had made "a gross error" and was "not of an acceptable standard" in carrying out his duties in Cambridgeshire in February 2008.
But he also criticised the "insufficient induction" he was given by Take Care Now as well as the NHS system which meant his skills were not properly assessed. The company's contract has now been terminated.
Mr Morris called for a review of European regulations which allow free movement of doctors, a national database of overseas doctors applying to work in out-of-hours services in the NHS, and more consistent standards in monitoring by local health chiefs working for primary care trusts.
A second patient Dr Ubani had treated - Iris Edwards, 86 - was ruled by the inquest to have died of natural causes.
Dr Ubani had had an application to work in the UK rejected by the NHS in Leeds because of inadequate English.
But he later got approval in Cornwall after they did not test his language skills.
Mr Morris also said there should be better assessment by the NHS of overseas doctors' ability to work in the UK.
Cambridgeshire Primary Care Trust issued a "profound apology" in court to the families of David Gray and other patients treated that day.
The PCT said Dr Ubani had delivered "substandard and dangerous treatment", and it apologised for "these failures and failures in the system".
Mr Gray's son Stuart, who is a GP, said: "My father's tragic death happened because of Dr Ubani's actions and because of serious failings within the Cambridgeshire Primary Care Trust and Take Care Now.
David Gray was given a huge overdose of the painkiller diamorphine
"We want to see him tried under UK law for his death but we also want safeguards put in place nationwide to prevent this happening again."
He added that proficiency in English should be an requirement for those applying to work as doctors in the UK and that there should be mandatory training before overseas doctors start work for the NHS and training on out of hours systems needs to be an essential part of that programme.
Peter Walsh, chief executive of Action Against Medical Accidents, said there are "systemic failings" which could affect anyone using out-of-hours care and called for an urgent wide-ranging review.
NICK TRIGGLE, HEALTH REPORTER BBC NEWS AT THE INQUEST
It was an innocuous setting from which from which to lay bare the failings of the out-of-hours GP system.
But the verdict given by William Morris at the coroner's court in the Cambridgeshire town of Wisbech could end up being the catalyst the system needs.
His 70-minute reading raised serious questions about the standards of care provided not only to David Gray but everyone who needs help at night and at the weekends.
The coroner did not leave anyone out. He criticised everyone from the government and General Medical Council down.
How was it, he asked, that a doctor who was unfamiliar with the NHS, whose first language was not English and who was tired from travelling from his home in Germany was allowed to see patients with very little support?
That, in a nutshell, is the crux of a very complex issue - and one that everyone involved in the system is now trying to answer.
"No-one in their right mind would design out-of-hours services the way they currently exist across England if they started with a blank piece of paper," he said.
Mr Gray was suffering from renal colic when he was given 10 times the normal amount of the painkiller diamorphine by Dr Ubani at his home in Manea, Cambridgeshire on February 16 2008, and was pronounced dead fours hour later, the hearing was told.
In April 2009, the German authorities gave Dr Ubani a nine-month prison sentence, suspended for two years, and he was ordered to pay a £4,500 fine for causing Mr Gray's death by negligence.
But he continues to practise as a cosmetic surgeon in the west German town of Witten.
The German conviction meant he could not be extradited to face possibly more serious charges in the UK.
Ms Edwards' case was not part of the criminal inquiry, although medical experts believe she was inappropriately treated and should have been sent to hospital.
Mr Gray's family are now appealing to the European Court of Human Rights as the German authorities have refused an extradition request because of the action taken against him.
Mike O'Brien: "We have to ensure we put in a better system than the one now."
The government, which had carried out a review of out-of-hours services in advance of today's verdict acknowledged improvements in the system were needed.
Changes will be made in the coming months but it is not yet clear whether they will meet the demands of the family or the coroner.
Dr David Colin-Thome who led the review said: "The quality of out-of-hours care for most people is better than it was in 2004 but there is unacceptable variation in how services are implemented and monitored around the country."
Responding to the coroner's inquest, Christine Braithwaite, head of investigation and enforcement at the CQC said: "The death of David Gray was a tragedy.
"It should not have happened and such an incident must not happen again.
"The coroner has clearly highlighted what went wrong.
"Take Care Now, and the PCTs that commission its services, must learn the lessons."
The Patient's Association said they had repeatedly called for PCTs to take their responsibilities on out-of-hours care seriously.
"The urgency of the out-of-hours situation is critical. Every PCT or equivalent throughout the UK should reassure their patients that the out of hours service for which they are paying is safe."
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.