Festival organizers said they hope Swinton's reputation and links with other celebrities such as George Clooney and Cate Blanchett will boost the fest's profile and connection, the Scotsman said Tuesday.
Swinton went to Fettes College in Edinburgh. She lives in Nairn with her husband, playwright and artist John Byrne.
Her screen debut was in Derek Jarman's "Caravaggio," and she has starred in Hollywood blockbusters and arthouse films.
"It is a sincere thrill for me to accept this honor," Swinton said. "Edinburgh, not only home to the most rocking arts festivals on the planet, is the nearest thing I have to a home town."
Connery, the event's sole patron since 1991, said Swinton is "one of the most intelligent, elegant and versatile actresses of our age and the range of her work, from arthouse to big, popular titles, mirrors that of the festival itself."
Noting the position is honorary, festival art director Hannah McGill said, "Sean's a global megastar, Tilda has unlimited respect; the two of them are a dream team."