Mr Bryden was an associate director at the National Theatre in London from 1975 to 1985, where his notable productions included The Mysteries, Larkrise, Candleford and the world premiere of David Mamet’s Glengarry Glen Ross.
He directed Son Of Man featuring Joseph Fiennes at the Royal Shakespeare Company’s Pit, while his West End productions included A Month In The Country starring Dame Helen Mirren and Sir John Hurt, and Life In The Theatre with Denholm Elliott and Sam West.
In a statement issued on Thursday, his family said: “The Scottish theatre director, playwright and television executive Bill Bryden died peacefully yesterday at the age of 79.”
Mr Bryden, born in Greenock, Inverclyde, was head of drama at BBC Scotland from 1984 to 1993, where he produced award-winning dramas including John Byrne’s Tutti Frutti with Dame Emma Thompson and Robbie Coltrane.
His theatre work included a production in 1990 when he wrote and directed The Ship in a former Harland & Wolff engine shed in Govan for Glasgow’s year as European City of Culture.
He also produced opera at the Royal Opera House – Parsifal and The Cunning Little Vixen – and The Silver Tassie at English National Opera.
Mr Bryden was made a CBE in 1993.
His family said while at the National Theatre, he worked notably with ensemble casts and created The Cottesloe Company, and was a loyal exponent of “promenade theatre”.
Figures from the arts have paid tribute to him.
Playwright David Greig tweeted: “So sorry to hear of the death of Bill Bryden, perhaps the greatest Scottish theatre director of his generation.
“His career covered everything from The Lyceum to The National to vast site-specific shows like The Ship & The Big Picnic. He took Scottish stories to the world.”
The National Theatre said on Twitter: “We’ve very sad to hear that director Bill Bryden has died.”
Mr Bryden is survived by his actress wife Angela Douglas, whom he married in 2009, and his two children Dillon and Kate from his first marriage in 1970 to Deborah Morris.