Graham, who was knighted in the 2021 New Year’s Honours, died on Saturday, the company said in a statement on Twitter.
His productions have been staged in cities around the world including Milan, New York, St. Petersburg, and Florence, according to its website.
The statement said: “We are devastated to announce that today 17 July 2021 Sir Graham Vick, Artistic Director, Birmingham Opera Company died of complications arising from Covid 19.
“We would ask all to respect the privacy of his partner and loved ones at this time.”
Graham’s career began in Scotland when he founded a small touring company to take opera to remote communities in the Highlands and Scottish islands, Birmingham Opera Company said.
In 1987 he founded the Birmingham Opera Company.
His production of Giuseppe Verdi’s Falstaff opened to the newly refurbished Royal Opera House in 1999.
Arts Council England paid tribute to Graham.
The public body wrote on Twitter: “Our deep condolences to the family, friends and colleagues of Sir Graham Vick.
“Having founded @BirminghamOpera some 34 years ago, he leaves an indelible mark on the opera community, the city of Birmingham, and the wider cultural sector.”
English National Opera added: “Everyone at the ENO is deeply saddened to hear the news of the death of Sir Graham Vick, the legendary opera director.
“It was our great pleasure to work with him on a number of landmark ENO productions including Madam Butterfly, Fidelio and the world premiere of Timon of Athens.”
By Tom Horton