The man - in his 60s - is the first person in the world to have the therapy, which was delivered at the Southern General Hospital in Glasgow at the weekend.
The patient was given a very low dose of the cells to determine whether the treatment is safe. A further 11 stroke patients will be given progressively higher doses during the next year to test for safety. Researchers will also look at whether the stem cells have started to repair the brain and improve their condition.
The start of the trial, led by Professor Keith Muir, was welcomed by campaigners and scientists across the UK.
Donated foetal brain cells were used in the early stages of the research, at the time prompting criticism from ethical campaigners. But the material used in the study has been created from stem cell lines derived from this one sample of foetal tissue seven years ago, meaning no more foetuses will need to be used.
The study - called Pilot Investigation of Stem Cells in Stroke (Pisces) - will monitor the patient closely for two years.
It will test whether implanting the stem cells can treat damaged areas of the brain and improve quality of life for victims of ischaemic stroke, the most common form of the condition, which is caused by a blockage of blood flow in the brain.
Prof Muir, from the University of Glasgow's Institute of Neuroscience and Psychology, said: "We are pleased that the first patient in the Pisces trial has undergone surgery successfully.
"Stroke is a common and serious condition that leaves a large number of people with significant disability.
"In this trial we are seeking to establish the safety and feasibility of stem cell implantation, which will require careful follow-up of the patients who take part. We hope that in future it will lead on to larger studies to determine the effects of stem cells on the disabilities that result from stroke."
The trial is being carried out with ReNeuron Group, which was given approval from the UK Medicines and Healthcare Products Regulatory Agency in January last year.
Dr Sharlin Ahmed, research liaison officer at the Stroke Association, said: "The use of stem cells to replace dead brain tissue is a promising technique which could help to reverse some of the disabling effects of stroke.
"We are very excited about this trial.However, we are at the beginning of a very long road and significant further development is needed before stem cell therapy can be regarded as a possible treatment."
Professor Chris Mason, chair of regenerative medicine bioprocessing at University College London, said: "This important clinical trial clearly demonstrates that the UK is capable of not only the very best stem cell research but also its translation into routine clinical practice."
Darren Griffin, professor of genetics at the University of Kent, said: "The news by the Glasgow team represents an important and exciting step with potential, in the long term, for treatment of a range of diseases."