Portuguese artist Rego, who was shortlisted for the Turner Prize in 1989 and whose portrait of Germaine Greer hangs in the National Portrait Gallery, has been made a Dame.
Mellon, who is president and co-founder of the Jimmy Choo designer shoe company, has received an OBE for services to the fashion industry.
Dunster is the founder of practice Zedfactory, which specialises in zero-carbon design and development. He has received an OBE for services for sustainable housing design.
Fashion photographer Nick Knight, who is founder of Show Studio and has worked with designers including Peter Saville, has received an OBE for services to art.
Also among those honoured are Margaret Mather Mineham, curriculum manager of Cleveland College of Art and Design, who picks up an MBE, and former Tate Britain director Dr Stephen Deucher, who picks up a CBE.
Richard Hunting, former chairman of the Geffrye Museum Trust and Peter Murray, founder and executive director of Yorkshire Sculpture Park, also receive CBEs.