A letter to the Times newspaper signed by more than 150 fellows of the Royal Society argues that leaving the EU would devastate research.
The researchers, including Prof Hawking, say that many promising young scientists were recruited from Europe.
They add that increased funding from Europe had benefitted UK science.
"First, increased funding has raised greatly the level of European science as a whole and of the UK in particular because we have a competitive edge," they wrote.
"Second, we now recruit many of our best researchers from continental Europe, including younger ones who have obtained EU grants and have chosen to move with them here."
The scientists said this situation encouraged the best scientists elsewhere to move to Britain.
The letter also cited the example of Switzerland which, despite paying into the EU has limited access to funds and - in their words - struggles to attract young talent because of restrictions on freedom of movement.
Prof Angus Dalgleish, of St George's Hospital, University of London, is a spokesman for "Scientists For Britain". This is a group of researchers arguing the case for an EU exit.
Last month, he told the BBC that he believed Britain would be no worse off on the outside.
"We are standing up against what is a very large body of people who feel that if we leave the EU it will be a disaster for funding and collaboration - and we completely refute that," he said.
"The bottom line is that we put far more into Europe than we get out. Any difference we can more than easily make up with the money we would save."
Prof Stephen Hawking has called for Britain to stay in the EU, saying that a Brexit would be a "disaster for UK science".