Mr Green, 40, who was dying from severe heart disease, was awaiting a transplant when his condition became so bad doctors decide to take action.
Instead of a real heart, the research scientist was given a pounds 100,000 full artificial replacement, the first person ever in this country.
There have been mechanical hearts in the past, but they have usually only replaced parts of the organ – and the patient needed to be plugged in permanently to a machine in hospital.
With the new portable heart, developed in America, Mr Green will be able to return home, walk the streets, and may even resume his nine mile cycle to work.
Yesterday the father-of-one and his wife Gill, 38, said they were looking forward to resuming normal family life in London for the first time in years with their five-year-old son Dylan.
Mr Green said: “Two years ago I was cycling nine miles to work and nine miles back every day but by the time I was admitted to hospital I was struggling to walk even a few yards.
"I am really excited about going home and just being able to do the everyday things that I haven't been able to do for such a long time such as playing in the garden with my son and cooking a meal for my family.
“I went for a pub lunch the other day and my son is just glad to have his dad back. My movement will still be limited but at least I can return home to be with my family.
“That means the world to me."
Mr Green suffered from a mysterious heart wasting disease called cardiomyopathia which rapidly destroyed the organ’s ability to pump blood around the body.
It meant he could hardly leave his bed and only a few steps left him totally breathless.
His only hope was a heart transplant but his condition worsened before a suitable donor became available.
Therefore doctors at Papworth Hospital, the world renowned heart centre near Cambridge, decided to give him Britain’s first ever full artificial heart.
During a six-hour operation in June, surgeons replaced Mr Green's damaged heart with the device which will serve the role of muscles and ventricles.
It provides a blood flow of up to 9.5 litres – about twice the rate of a normal heart when the body is at rest.
Unlike previous artificial hearts, the new one is powered by a pump which sits outside the body and can be held in a backpack or shoulder bag.
All Mr Green has to do is replace the batteries in the pump every few hours and the heart should last up to three years.
Steven Tsui, the consultant cardiothoracic surgeon who carried out the operation, said the heart, designed by a company called SynCardia, was only meant to be a “bridge” while a real heart was found.
But it was a step closer to a permanent artificial heart being developed. Mr Tui said: “For the first time we are going to have a person walking the streets of Britain without a human heart.
“We believe that there are many patients that could benefit from this device. Matthew was very sick and we were worried he was running out of time.
“He was barely able to walk a few yards before getting breathless and his kidney and liver were suffering.
“Since the operation he has been given a completely new lease of life. He used to be able to cycle to work every day. I expect him to be able to do that again.
“This shows that technology can triumph over illness. I expect more and more of these devices to be developed.”
Papworth Hospital is the only centre in the UK currently allowed to implant this type of device.
In November 1986, a British patient received an artificial heart and was supported for two days before undergoing a heart transplant.
Professor Peter Weissberg, medical director at the British Heart Foundation, said: "With this artificial heart, the power supply is small enough to fit in a shoulder bag so patients can walk around and go home."
File photo of an artificial heart 
A 40-year-old man from the United Kingdom has survived an operation in which he was given a wholly artificial heart. It is believed that this is the first time in the UK that a patient has been able to return home with such an implant.

Matthew Green, a father of one, experienced the operation in , located in , England. His health has declined over the last few years, and he has suffered a substantial heart disorder, identified as . He is waiting to have a human heart implanted. The disease would have claimed his life had the operation to implant a plastic heart not occurred. Approximately nine hundred operations of this nature have already taken place worldwide.

Having survived the transplant, Green stated that the plastic heart will "revolutionise" his life. "Before I couldn't walk anywhere," commented Green. He described his ability "to be with normal people again" as "fantastic". Having the opportunity to live a relatively regular life "means the world" to Green.

Providing a nine-and-a-half litre blood flow at its peak, the plastic heart can provide roughly twice that of a resting human body. The artificial heart was implanted last June in a six-hour operation. Unlike other mechanical hearts, Green's heart is powered by a pump that can be transported in a handheld bag.