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Prof Higham is the deputy director of the Oxford Radiocarbon Accelerator Unit, at Oxford University, England, and is a University of Otago graduate in archaeology.
The researchers undertook high-precision dating of materials from 40 archaeological sites, from Russia to Spain.
This revealed Neanderthals disappeared from Europe about 40,000 years ago, the researchers said.
Rather than a rapid replacement of European Neanderthals by anatomically modern humans, the study, published in Nature, supported a ''more complex picture'', and a ''biological and cultural mosaic that lasted for several thousand years''.
Neanderthals and modern humans were both living in Europe for between 2600 and 5400 years, the research suggested.
For the first time, researchers had constructed a ''robust timeline'' showing when the last Neanderthals died out, information which had eluded scientists previously, Prof Higham said in an interview. Evidence suggested Neanderthals disappeared at different times across Europe rather than being rapidly replaced by modern humans.
The results had involved a ''huge amount of work'', and the research team obtained new radiocarbon dates for about 200 samples of bone, charcoal and shell.
Prof Higham, who has a BA (Hons) and an MA in archaeology from Otago University, said that his fascination with Neanderthals began within the first few weeks of his Otago studies.
One of the ''big questions'' in this field had been ''what happened when modern humans and Neanderthals met'', and a ''reliable chronology'' was needed to understand this.
The researchers had now shown that modern people in Europe were sharing the continent with Neanderthals for ''much longer than previously thought'', with sufficient time for cultural influence and interbreeding.
Other recent studies suggested modern human and Neanderthal groups interbred outside Africa, with at least 1.5% of the DNA of modern non-African human populations originating from Neanderthals, researchers said. firstname.lastname@example.org