Experts at University College London say the new nose will look exactly the same as the man's original one, and hope it will even have a sense of smell.
The trial marks the first time a full nose has been grown from scratch, and could in future be used as a therapy for patients such as soldiers and car crash victims, the Daily Mail reported.
The first stage of the process was to create a glass mould of the unnamed man's nose, and to spray it with a honeycomb-like material to form a biological scaffold for new cells to attach themselves to.
Once the scaffold had been built, the glass mould was removed and the biological frame was coated with millions of stem cells which can be coaxed into forming cartilage using chemicals.
At the same time, researchers inserted a small balloon beneath the surface of the man's arm and gradually inflated it to stretch the skin, making it loose enough to accommodate the new nose.
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Two months ago, the framework bearing the stem cells was inserted under the skin in place of the balloon, and now resides in the man's arm where it is growing new networks of nerves, blood vessels and skin.
After three months beneath the man's skin, the nose will be ready for removal and can be surgically reattached to his face, allowing the arm to be sewn up and returned to normal.
The project is similar to a famous 1990s experiment in which American researchers attempted unsuccessfully to grow ears on a mouse for use in transplants.
Professor Alex Seifalian, who is leading the experiment, said the man's nose has been designed to look exactly like the original – slightly crooked.
He told BBC Focus magazine: "His nose was a little bit bent to the left and we asked if he wanted it straight but he said no, he wanted it exactly the same."