Oxford and Cambridge university scientists believe it belongs to a species closely related to Iguanodon, a large herbivore which had a long tail for balance and hind legs that were longer than their fore limbs.
And their brains displayed distinct similarities to the brains of modern-day crocodiles and birds.
Meninges - the tough tissues surrounding the actual brain - as well as tiny capillaries and portions of adjacent cortical tissues have been preserved as mineralised 'ghosts'.
Co-author Dr Alex Liu of Cambridge's Department of Earth Sciences said: "The chances of preserving brain tissue are incredibly small, so the discovery of this specimen is astonishing."
The reason this particular piece of brain tissue has been so well-preserved is that the dinosaur's brain was essentially "pickled" in a highly acidic and low-oxygen bog or swamp shortly after its death.
This allowed the soft tissues to become mineralised before they decayed.
The study was published in a Special Publication of the Geological Society of London in tribute to the late Professor Martin Brasier of the University of Oxford, who died in 2014.
Dr David Norman from the University of Cambridge co-ordinated the research, along with the late Professor Brasier during the years prior to his untimely death in a road traffic accident.
Dr Norman said: "What we think happened is that this particular dinosaur died in or near a body of water, and its head ended up partially buried in the sediment at the bottom.
"Since the water had little oxygen and was very acidic, the soft tissues of the brain were likely preserved and cast before the rest of its body was buried in the sediment."
Working with colleagues from the University of Western Australia, the researchers used scanning electron microscope (SEM) techniques to identify the tough membranes, or meninges, that surrounded the brain itself, as well as strands of collagen and blood vessels.
Structures that could represent tissues from the brain cortex, its outer layer of neural tissue, interwoven with delicate capillaries, also appear to be present.
The structure of the fossilised brain, and in particular that of the meninges, shows similarities with the brains of modern-day descendants of dinosaurs, namely birds and crocodiles.
In typical reptiles, the brain has the shape of a sausage, surrounded by a dense region of blood vessels and thin-walled vascular chambers (sinuses) that serve as a blood drainage system.
The brain itself only takes up about half of the space within the cranial cavity.
In contrast, the tissue in the fossilised brain appears to have been pressed directly against the skull, raising the possibility that some dinosaurs had large brains which filled much more of the cranial cavity.
Dr Norman warned not to draw any conclusions about the intelligence of dinosaurs from this particular fossil.
It was most likely that during death the head of this dinosaur became overturned, so that as the brain decayed, gravity caused it to collapse and become pressed against the bony roof of the cavity.
Dr Norman said: "As we can't see the lobes of the brain itself, we can't say for sure how big this dinosaur's brain was.
"Of course, it's entirely possible that dinosaurs had bigger brains than we give them credit for, but we can't tell from this specimen alone.
"What's truly remarkable is that conditions were just right in order to allow preservation of the brain tissue - hopefully this is the first of many such discoveries."
Co-author Mr Hiscocks added: "I have always believed I had something special.
"I noticed there was something odd about the preservation, and soft tissue preservation did go through my mind.
"Martin realised its potential significance right at the beginning, but it wasn't until years later that its true significance came to be realised.
"In his initial email to me, Martin asked if I'd ever heard of dinosaur brain cells being preserved in the fossil record.
"I knew exactly what he was getting at.
"I was amazed to hear this coming from a world renowned expert like him."
