Prof. Higham says recent genetic studies show up to 2% of DNA in today's non-African humans is Neanderthal in origin, suggesting the two groups did interbreed outside Africa.
First author Tom Higham, a professor in Oxford's School of Archaeology, and colleagues describe how they compiled the timeline in the journal Nature.
One of their most significant findings suggests that modern humans did not rapidly replace Neanderthals, but that our ancestral cousins disappeared at different times across Europe.
For the 6-year study, Prof. Higham and colleagues used improved methods of radiocarbon dating to analyze about 200 samples of bone, shell and charcoal from 40 important archeological sites around Europe, ranging from Russia to Spain.
The sites were chosen because they either showed signs of Neanderthal tool-making, which archeologists describe as "Mousterian sites," or because they contained stone tools thought to be from early modern humans or Neanderthals - so-called "transitional sites."
Using mathematical models, the team compared the new radiocarbon data with previous findings from studying rock layers, to piece together the chronology of the findings.
The results show that Neanderthals disappeared from Europe between 41,030 and 39,260 years ago, which is long after early modern humans arrived.
This means, say the authors, that Neanderthals and early modern humans must have overlapped for a significant period, giving enough time for them to interact and interbreed.
However, they point out they were not able to determine exactly where in Europe interbreeding may have occurred, and whether it happened just once or repeatedly.
Play the video below to see Prof. Higham explain the team's findings.
Prof. Higham says recent genetic studies show up to 2% of DNA in today's non-African humans is Neanderthal in origin, suggesting the two groups did interbreed outside Africa, and adds:
"We believe we now have the first robust timeline that sheds new light on some of the key questions around the possible interactions between Neanderthals and modern humans."
Neanderthals may have survived in dwindling pockets across Europe
He says the evidence also suggests Neanderthals "may have survived in dwindling populations in pockets of Europe before they became extinct," and that contrary to current beliefs, there may have been a more complex picture about which groups influenced the tool-making industrial period that followed the Mousterian. Prof. Higham says this picture is "characterized by a biological and cultural mosaic that lasted for several thousand years."
Prof. Higham says previous techniques for obtaining radiocarbon dates may have resulted in underestimates of the age of Neanderthal samples, which could have been contaminated with modern material.
"We used ultrafiltration methods which purify the extracted collagen from bone, to avoid the risk of modern contamination," he explains, adding that:
"This means we can say with more confidence that we have finally resolved the timing of the disappearance of our close cousins, the Neanderthals. Of course the Neanderthals are not completely extinct because some of their genes are in most of us today."
In January 2014, Medical News Today reported how another Nature study led by geneticists at Harvard Medical School, suggests ways in which the genetic legacy of the Neanderthals has proven to be both adaptive and maladaptive for modern humans.