Heatherwick, whose cauldron design were kept top secret until it was unveiled at the end of the Olympic opening ceremony on 27 July 2012, has been awarded a CBE.
Barber and Osgerby, whose consultancy created the Olympic Torch that travelled the UK in the run-up to the Olympics, both receive OBEs.
All have been recognised for services to the design industry.
Meanwhile sculptor Anish Kapoor, who created the ArcelorMittal Orbit installation in the Olympic Park with Cecil Balmond, has been given a knighthood.
And a non-Olympic design honour goes to Graven Images co-founder Janice Kirkpatrick, who receives an OBE for services to graphic design.