The "bio-glue" is incredibly strong, moves with the body and crucially, sticks to wet surfaces.
The team at Harvard University have even used it to seal a hole in a pig's heart.
Experts have described the glue as "really cool" and said there would be "absolutely huge demand" for it.
Getting something to stick to a damp surface has been a huge challenge - think what happens when you get a plaster on your finger wet.
The university's Wyss Institute for Biologically Inspired Engineering turned to the "Dusky Arion" slug, which creates sticky mucus as a defence against predators.
"We engineered our material to take on the key features of slug mucus and the result is really positive," researcher Dr Jianyu Li said.
The bio-glue they produced has two components - the actual adhesive and a biochemical "shock absorber".
The incredible stickiness comes from the trinity of the attraction between the positively charged glue and negatively charged cells in the body; covalent bonds between atoms in the cell surface and the glue, and the way the glue physically penetrates tissue surfaces.
But it is the shock-absorbing component that is crucial - it takes the physical stress and strain, so the adhesive component stays stuck.
Experiments, published in the journal Science, show the glue is not toxic to living tissue and is three times stronger than any other medical adhesive.
Dr Li told the BBC News website: "I'm really amazed by this system. We have solved a big challenge and opened up big opportunities in the medical setting.
"The applications are pretty broad - the material is very tough, stretchy and compliant, which is very useful when you want to interface with a dynamic tissue like the heart or lungs."
It could be used as a patch on the skin or as a liquid injected into wounds deeper in the body.
There are also ideas about using it as a way of releasing drugs to specific parts of the body or to stick medical devices to organs like those to help the heart beat.
The glue adheres to a surface within three minutes, but then gets stronger. Within half an hour it is as strong as the body's own cartilage.
Dr Chris Holland, from the department of materials science and engineering at the University of Sheffield, said: "It's really cool, I must admit.
"It is clear it outperforms the alternatives on the market and oh my goodness, there is potentially absolutely huge demand.
"They are still at an early stage, but this kind of thing could be part of a surgeon's standard kit."
But there is not yet a technology ready for medical use.
So far it has proven its capabilities mechanically in the laboratory, in tests on rats and by sealing a hole in a pig's heart through tens of thousands of simulated heartbeats.
The Wyss Institute, which has applied for a patent, says the glue is cheap to make.
It is also working on biodegradable versions that would naturally disappear as the body heals.
Prof John Hunt, the research theme lead for medical technologies and advanced materials at Nottingham Trent University, told the BBC: "The need for new adhesives as glues or tapes is clear to all healthcare providers.
"This one has the potential to improve healthcare and save lives.
"This research is really exciting [but] the detail of the biocompatibility will need to go beyond what is presented in the paper to guide the long-term clinical efficacy, safety, and therefore the real medical applications."
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A defensive mucus secreted by slugs has inspired a new kind of adhesive that could transform medicine, say scientists.