The awards are the first to be given at Edinburgh for a number of years, after the competitive aspect of the festival was disbanded, only to be reinstated by new festival director Chris Fujiwara for 2012.
According to The Hollywood Reporter, the Michael Powell Award for Best British Feature Film was awarded to Penny Woolcock's One Mile Away, which made its world premiere at the festival.
A jury headed by actor Jim Broadbent described the film, a documentary about warring street gangs in Birmingham, as "brave and honest", and "a singular achievement".
The international jury was chaired by Elliot Gould, and crowned Mao Mao's Here Then, a story of disillusionment amongst Chinese youth, as the 'Best International Film'.
Andrea Riseborough and Brid Brennan jointly won the award for 'Best Performance in a British Film' for their roles in James Marsh's IRA thriller Shadow Dancer.
The festival opened with the UK premiere of William Friedkin's Killer Joe, and closes tomorrow night (July 1) with the European premiere of new Pixar filmBrave.
Watch the trailer for Shadow Dancer below: