Doran, who told Whatsonstage.com that Boyd was leaving “very big shoes to fill,” will formally take the reins following the RSC's annual general meeting in September.
The RSC board have not yet named Heywood's successor, with news of that appointment expected next month.
In a press statement about the appointment, chair of the RSC's board Nigel Hugill said: "Greg Doran is a perfect choice for the RSC and is well known to all our audiences. His long history with the Company is testament to his great skill as a director, his deep understanding of Shakespeare and a true commitment to theatre-making.
"He has directed many award-winning productions and seasons at the RSC, and taken our work right across the world, receiving recognition for his talent as far afield as the US, Japan, Spain and South Africa, as well as in the UK. He has championed the classical repertoire and new work alongside Shakespeare, and has been a long-time collaborator with many RSC artists. As well as directing theatre, he has led the way in experimenting with capturing theatre on film and has written extensively about Shakespeare."
In 2002, Doran led a season of five seldom-performed Jacobean and Elizabethan plays and directed The Island Princess by John Fletcher. The production enjoyed sell out season at the Swan Theatre and a run at the West End's Gielgud Theatre, receiving an Olivier Award for Outstanding Achievement of the Year.
In 2005 he led the "Gunpowder" season in the Swan, directing Ben Jonson's Sejanus in this season of neglected Jacobean works.
This year Doran directs Julius Caesar for the World Shakespeare Festival and The Orphan of Zhao. His most recent RSC productions include: Written on the Heart, Cardenio, Morte d'Arthur, Twelfth Night, Hamlet, A Midsummer Night's Dream and Love's Labour's Lost.
His other productions for the RSC include: Macbeth, Antony and Cleopatra, Coriolanus, All's Well That Ends Well, The Taming of the Shrew (and The Tamer Tamed), Much Ado About Nothing, The Winter's Tale, Othello, Merry Wives The Musical, The Merchant of Venice, As You Like It, King John, Timon of Athens, All Is True (Henry VIII), Venus and Adonis (in collaboration with The Little Angel Theatre), Rostand's Cyrano de Bergerac, Oroonoko by Biyi Bandele (after Aphra Behn), The Odyssey adapted by Derek Walcott, Jubilee by Peter Barnes, and The Canterbury Tales in an adaptation by Mike Poulton.
Commenting on Doran's appointment Michael Boyd said in a press statement: "This is fantastic news and I’m very pleased to be leaving the Company in such good hands. I know this is a choice which will be wholeheartedly welcomed by our staff, artists and audiences.
I have been fortunate to work with Greg as an associate director throughout my leadership of the RSC. He is a first rate director, and nobody knows and loves the company more than him. I will be programming work for 2013 over the course of the summer, in order to allow him breathing space to plan for the future. I wish him every good fortune in a role which I have been lucky enough to undertake over the last decade."
The selection panel for Boyd's replacement was led by the RSC's chairman Nigel Hugill and included David Tennant, who Doran directed as a record-breaking and Whatsonstage.com Award-winning in Hamlet in 2008.
Reflecting on his appointment, Gregory Doran said: “I am delighted to be appointed as artistic director of this great company. I joined the RSC 25 years ago, first as an actor, then as assistant director and then chief associate, so I guess if my appointment represents something, it represents a long term commitment to the disciplines and craftsmanship required to do the astonishing plays of our 'Star of Poets', William Shakespeare.
“Michael Boyd and Vikki Heywood have done an exceptional job in the last decade, rebuilding the theatre and reasserting the principles of ensemble and collaboration, which I hope to continue and extend. My first task is to assemble an exciting new artistic team, with whom I shall start planning the Company’s future from 2014.”