The tiny hollow "organoids", measuring three to four millimetres across, have a structure similar to that of an immature human brain, including defined regions.
But the scientists insist they are still far from the science fiction fantasy of building a working artificial brain - or even replacement parts for damaged brains.
The goal was to produce a biological tool that can be used to investigate the workings of the brain, better understand brain diseases, and test out new drugs.
Other experts described the work as "audacious", "exciting" and "stunning".
One predicted the future creation of a simple animal-like brain that could be linked to sense organs and had the ability to learn.
Scientists have previously grown other laboratory "models" of human organs from stem cells, including those replicating the liver, intestine, pituitary gland and eye. But none possess the daunting intricacy of the human brain, the most complex structure in the universe.
The key to the new research involved nourishing immature cells in a gel-like "matrix" that allowed the complex organoid structures to develop.
These were then transferred to a spinning bioreactor which provided extra nutrients and oxygen, enabling them to grow much larger in size.
After two months of development the "mini-brains" had become globular spheres up to four millimetres in diameter. Each one surrounded a ventricle-like inner cavity and mimicked the layered structure of a human brain growing within a developing foetus.
Among the identifiable regions were a cerebral cortex, forebrain, choroid plexus - the body that produces cerebro-spinal fluid - and even a rudimentary retina. Tests showed that they contained active neurons.
The raw material the scientists started with consisted of human stem cells - immature cells with the potential to develop along many different pathways.
Both embryonic stem cells, originating from early-stage embryos, and artificially "reprogrammed" skin cells known as induced pluripotent stem cells (iPS) cells were employed.
In a further experiment to show the technique's potential, the researchers used cells taken from a patient with the brain disease microcephaly to create the mini-brains.
They found that the organoids' growth was stunted, mimicking the disease which causes the brain to be much smaller than normal.
Professor Juergen Knoblich, from the Institute of Molecular Biotechnology in Vienna, who led the Austrian and British team, said: "We've been able to model one disease which is microcephaly. But ultimately we'd like to move to more common disorders like schizophrenia or autism. We are confident that we might be able to model some of these defects."
He said the extreme complexity and inter-connectivity of the adult brain made him "pessimistic" about the possibility of replacing whole brain structures with laboratory-grown versions.
Prof Knoblich added: "Our system is not optimised for generating an entire brain and that is also in no way our goal."
Although the organoids were small, they were not very different in size from an early stage developing brain in the womb.
"This is one of the cases where size doesn't really matter," said the professor.
Scientists commenting on the research, published in the online edition of the journal Nature, spoke of its potential and implications, but also limitations.
Dr Dean Burnett, lecturer in psychiatry at the University of Cardiff, said: "Saying you can replicate the workings of the brain with some tissue in a dish in a lab is like inventing the first abacus and saying you can use it to run the latest version of Microsoft Windows; there is a connection there, but we're a long way from that sort of application yet."
Dr Martin Coath, from the Cognition Institute at the University of Plymouth, questioned why anyone would ever want to create a "real" human brain.
"A human brain that was 'fully working' would be conscious, have hopes, dreams, feel pain, and would ask questions about what we were doing to it," he said. "Something we have grown in the lab, but on a much simpler level than a human brain, might be hooked up to electronic eyes, ears, and hands and be taught to do something - maybe something that is as sophisticated as many simple living creatures. That doesn't seem so far off to me."
Neuroscientist Professor Paul Matthews, from Imperial College London, said: "This study offers the promise of a major new tool for understanding the causes of major developmental disorders of the brain such as autism and schizophrenia, as well as testing possible treatments. Treatments are still a long way off, but this important study illuminates part of the pathway to them."
Stem cell scientist Dr Zameel Cader, from Oxford University and the John Radcliffe Hospital, described the research as "fascinating and exciting".
He added: "The structure they have generated is a long way from a real brain and the challenges for creating even a primitive foetal brain remain daunting. Hopes to recreate a real brain therefore remain distant. The proper organisation and blood supply of the brain are not present in this model and are major limitations.
"However, their model is audacious and the similarities with some of the features of a human brain are really quite astounding."