In total, 12 patients will get ReNeuron's ReN001 cell therapy between six and 24 months after having an ischaemic stroke - caused by a blockage of blood flow in the brain - and their progress will be followed for two years.
The study will initially examine the safety and feasibility of the treatment.
If successful, researchers plan to develop the trials to focus on more severely disabled stroke patients.
About half of all stroke survivors are left with permanent disabilities as a result of brain damage.
The potential of different kinds of stem cells - master cells that can develop into specialised tissue in the body - is being examined by experts around the world for many diseases.
But the technology is controversial, in part because some stem cell lines are derived from embryos or foetuses.
The Society for the Unborn Child, a British-based pro-life charity, said last month that proposed trial was "sick".
"It is unethical in every way - killing one member of the human race to help another. We are totally opposed to this," the BBC quoted a spokesperson as saying.
Stem cells are the master cells of the human body from which all other cells - such as brain, blood, heart muscle or bone cells - are created.
Stem cells are considered to be unique because they are the only type of cells which have the ability to divide into daughter cells.
Daughter cells can then be used to create more stem cells or specialised cells, those tasked with a particular function within the human body.