The prince takes over the role from The Queen as the international festival celebrates its 70th anniversary.
In December, Buckingham Palace announced the Queen would stand down as patron of 25 organisations, including the International Festival, at the end of her 90th year.
International Festival Director Fergus Linehan said: "We are thrilled."
He added: "His Royal Highness has a great interest in performing arts and we look forward to welcoming him to see some of the world's greatest artists and ensembles here in Edinburgh."
"On behalf of the Trustee Board and staff of the International Festival, I'd like to thank The Queen for her longstanding support.
"Her Majesty often visited the international festival alongside members of the Royal family and we are delighted that this family connection continues as we welcome The Earl of Wessex as our third Royal patron."
Prince Edward The Earl of Wessex has become Royal patron of the Edinburgh International Festival.