The Wellcome Trust is the second biggest charitable funder of medical research after The Bill Gates Foundation, and last year agreed a deal to publish on the internet research papers from major scientific institutions.
It is currently converting its offices on London's Euston Road into an exhibition centre to be opened this year.
'The trust distributes over £455m in grants every year, and my role is to make both the public and the scientific community aware of the work that that money is funding,' said Randall.
In April, Randall will be joined by University of Edinburgh PR and press manager Katrina Nevin-Ridley, who is taking over the head of media role. She replaces Barry Gardener, who left to go freelance at the end of February.