Dr Gibson, who is based at the Institute of Education in Cambridge, won the Sam Wanamaker International Shakespeare Globe Award, named to honour the founder of the Shakespeare Globe Trust, who died in London in 1993.
The other winners were Robert Stephens (The Sir John Gielgud Award for Best Actor); Penny Downie (The Dame Peggy Ashcroft Award for Best Actress), Matthew Warchus (The Richard Burton Award for Most Promising Newcomer), Thelma Holt (The Sir Tyrone Guthrie Award for Best Production), and Adrian Noble (The Peter Brook Award for Best Director).